Huntianyi zhu 渾天儀注

Huntianyi tuzhu 渾天儀圖注, also called Huntianyi zhu 渾天儀注 "(Illustrated) Commentaries on the armillary sphere" or Zhang Heng hunyi 張衡渾儀, was a book on an armillary sphere constructed during the Later Han period 後漢 (25-220 CE) by Zhang Heng 張衡 (78-139 CE), who also wrote another theoretical book on astronomy, Lingxian 靈憲. However, some scholars doubt that Zhang was the author of the Huntianyi zhu. The book with an original size of 1 juan has only survived in fragments assembled in Hong Yixuan’s 洪頤煊 (1765-1837) series Wenjingtang congshu 問經堂叢書 (part Jingdian jilin 經典集林) and Ma Guohan's 馬國翰 (1794-1857) Yuhan Shanfang jiyi shu 玉函山房輯佚書.

The astronomical chapter (19 Tianwen zhi 天文志) in the history book Suishu 隋書 describes the bronze armillary sphere Zhang Heng constructed. He used a quarter-degree system for measurements. The circumference of the celestial sphere was 1 zhang, 4 chi, 6 cun, and 1 fen (see weights and measures). Inside a sealed chamber, he used a water-driven mechanism to rotate the sphere. An observer was stationed inside, doors closed, to track the movements and announce them. These announcements were then relayed to the astronomers at the Lingtai Observatory 靈臺. Whenever the spherical rings aligned with a particular star, the observer would report if a certain star has just appeared reached its meridian or has set. Each observation was found to match perfectly with celestial predictions.

The apocryphal text Chunqiu wenyao gou 春秋文曜鉤 holds that during the reign of Emperor Yao 堯, the astronomer Xi He 羲和 established the armillary sphere, marking the early origins of astronomical instruments. In the Taichu reign-period 太初 (104-101) of the Han dynasty, Luo Xiahong 落下閎 (156—87 BCE), Xianyu Wangren 鮮于妄人 and Geng Shouchang 耿壽昌 constructed a spherical instrument to study celestial measurements. Later, during the Yongyuan reign-era 永元 (89-104), Jia Kui 賈逵 (30-101 CE) created a bronze armillary sphere specifically designed to track the ecliptic. Zhang Heng later continued this tradition by constructing his armillary sphere. Liu Hong 劉洪 (c. 130-196), Lu Ji 陸績 (188-219), and Wang Fan 王蕃 (228-266) successively improved these instruments, making them increasingly precise and sophisticated over time.

The Huntianyi zhu presents a vision of the universe with the following structure: The celestial sphere is like a ball, perpetually rotating (hunhun 渾渾). The Earth is likened to the yolk of an egg, while the heavens resemble the eggshell. Within the heavens, there is water, which occupies half of the celestial sphere, and the Earth floats upon this water. The analogy of Earth as the yolk has led to differing interpretations among modern scholars. One view considers this an early conceptualisation of the Earth as a sphere, marking the origins of the round-earth theory (diyuan shuo 地圓説) in China. Another view argues that before Western astronomy was introduced in the late Ming period 明 (1368-1644), ancient Chinese cosmology never embraced the idea of a spherical Earth. According to this interpretation, even later versions of the Spherical-Heaven Theory (huntian shuo 渾天說) adhered only to the flat-earth model (diping shuo 地平説). To this day, the debate between these two perspectives continues.

Moreover, the idea of a hard celestial shell was indispensable and highly practical for calculations. If considering the statement from the Lingxian that "the outer bounds of the universe are infinite, and the ends of space are endless", then the limits of the cosmos are not confined by a celestial shell (tianke 天殻). Instead, it seems to suggest the existence of layers of "heavens beyond the heavens". The Spherical-Heaven Theory holds that the celestial sphere is 365 ¼ degrees in total (and not 360°). If divided in half; 182 ⅛ degrees are exposed above the Earth, while the other half remains below. This explains why half of the 28 lunar mansions are visible at any given time while the other half is hidden.

The celestial equator encircles the celestial sphere at its midsection, positioned 91.5 degrees from both poles (more precisely, 91 degrees and 5/16 of a degree). It runs in the southeastern direction, wrapping around the middle of the heavens. The ecliptic, however, is tilted relative to the celestial equator, intersecting it at an angle of 24 degrees. According to modern measurements, the axial tilt in 100 CE was 23.685 degrees, differing by only 0.03 degrees, demonstrating the remarkable precision of ancient Chinese calculations.

During the winter solstice, the southernmost point of the ecliptic lies 24 degrees beyond the celestial equator, marking its outer boundary. During the summer solstice, the northernmost point of the ecliptic lies 24 degrees inside the celestial equator, marking its inner boundary. At the winter solstice, the Sun is positioned 21 degrees south in the constellation Dou (斗宿; approx. Sagittarius) and is 115 ⁵⁄₁₆ degrees from the celestial pole. During this time, the Sun travels 146 degrees above the Earth (daytime) and 219 degrees below the Earth (nighttime). At the summer solstice, the Sun is 25 degrees north in the constellation Jing (井宿; approx. Gemini) and is 67 ⁵⁄₁₆ degrees from the celestial pole. During this time, the Sun travels 219 degrees above the Earth (daytime) and 146 degrees below the Earth (nighttime). The ecliptic intersects the celestial equator at two points: the spring equinox and the autumn equinox. Both points are 91 ⁵⁄₁₆ degrees from the celestial pole. At the spring equinox, the Sun is slightly more than 14 degrees in the constellation Kui (奎宿; approx. Pisces). At the autumn equinox, the Sun is somewhat less than 5 degrees in the constellation Jiao (角宿; approx. Virgo). During both equinoxes, the Sun spends 182 ⁵⁄₁₆ degrees above the Earth (daytime) and 182 ⁵⁄₁₆ degrees below the Earth (nighttime).