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Qiongtianlun 穹天論 "Arched-Heaven Theory" is a cosmological and astronomical theory created during the Jin period 晉 (265-420) by Yu Song 虞聳, courtesy name Shilong 世龍, from Yuyao 餘姚 (in today's Zhejiang province). He was the sixth son of the renowned scholar Yu Fan 虞翻 (164-233), who was highly knowledgeable in astrology and literature, and authored a commentary on the Zhouyi 周易. In the literary world, he was considered on par with Kong Rong 孔融 (153-208). From a young age, Yu Song was influenced by his father and acquired extensive learning. He particularly enjoyed associating with reclusive scholars who lived in seclusion and obscurity and despised extravagance and instead promoted frugality.
Fragments of the book quoted in the treatise on astronomy (11-13 Tianwen zhi 天文志) in the history book Jinshu 晉書 were assembled by Ma Guohan 馬國翰 (1794-1857) and are found in his series Yuhanshanfang jiyi shu 玉函山房輯佚書. The Song-period 宋 (960-1279) encyclopaedia Taiping yulan 太平御覽 quotes from Yu Bing's 虞昺 Qiongtianlun and Tianwenlu 天文錄. Yu Bing was a younger brother of Yu Song. However, Li Chunfeng's 李淳風 (602-670) astrological book Yisizhan 乙巳占 also takes Yu Song as the author of the Qiongtianlun. In his commentary Yueling zhengyi 月令正義, Kong Yingda 孔穎達 (574-648) therefore concludes that the personal name of the author cannot be told with certainty. The Tang-period 唐 (618-907) encyclopaedia Beitang shuchao 北堂書鈔 names the author Yu Shihong 虞世洪, which might be an error for Yu Shilong 虞世龍.
| 天形穹隆如鷄子，幕其際，周接四海之表，浮於元氣之上。譬如覆奩以抑水，而不沒者，氣充其中故也。 | The shape of the heavens is arched like an egg, covering its boundaries like a canopy. It surrounds the edges of the Four Seas and floats above the primordial ether (yuanqi 元氣). It is like an inverted container pressed onto water—yet it does not sink, because the ether within supports it. |
| 日繞辰極，沒西而還東，不出入地中。天之有極，猶蓋之有斗也。天北下於地三十度，極之傾在地卯酉之北亦三十度，人在卯酉之南十餘萬里，故斗極之下不爲地中，當對天地卯酉之位耳。 | The sun revolves around the celestial pole, setting in the west and returning to the east, without actually entering or emerging from beneath the earth. The heavens have a central axis, much like a canopy has a handle. The northern part of the sky is tilted downward toward the earth by 30 degrees, and the celestial pole is inclined 30 degrees to the north of the east-west (mao-you 卯酉) axis of the earth. Since people live more than a hundred thousand li "miles" south of this axis, the area beneath the celestial pole does not correspond to the center of the earth but rather aligns with the east-west positions of heaven and earth. |
| 日行黃道繞極，極北去黃道百一十五度，南去黃道六十七度，二至之所舍以爲長短也。 | The sun moves along the ecliptic, circling the celestial pole. The pole is positioned 115 degrees north of the ecliptic and 67 degrees south of it. The points where the sun resides during the two solstices determine the varying lengths of day and night. |
The Qiongtianlun posits that the shape of the heavens is curved like an eggshell, with the celestial canopy extending to the edges of the Four Seas. The space between the earth and the celestial shell is filled with ether (qi 氣), preventing the heavens from collapsing.
Overall, the Qiongtianlun still falls within the framework of the Canopy-Heaven Theory (gaitian shuo 蓋天說). However, it introduces some new perspectives in specific details. For instance, the claim that the earth is surrounded by oceans on all sides draws from Zou Yan's 鄒衍 (c. 305-240 BCE) theory of the great nine continents (da jiuzhou shuo 大九州說) from the Warring States period. The intention behind this idea was likely to provide a better explanation for how the round heavens and the square earth could connect at their boundaries, addressing doubts left by earlier theories.
Additionally, it incorporates the concept of qi to explain why the celestial shell does not collapse, using the analogy of an inverted box floating on water, which adds a degree of persuasiveness. This suggests an element of analogical reasoning and empirical observation, rather than being a purely speculative or unfounded theory. This brings the Arched-Heaven Theory into the vicinity of the Xuanye Theory (xuanye shuo 宣夜説) which also hold that qi was the fundamental substance supporting celestial bodies. Although their specific explanations differ, their core concept remains the same. This marks a clear advancement over the older Canopy-Heaven Theory, which relied on ideas like celestial pillars to support the sky.
Furthermore, the Qiongtianlun introduces imaginative new ideas, such as the assertion that the area beneath the North Pole is not the exact center of the earth and that the sun does not actually enter the ground but instead revolves around the North Pole, setting in the west and returning in the east. Additionally, the treatise provides specific astronomical measurements, such as "the northern sky tilts 30 degrees downward toward the earth." This roughly corresponds to observations from Jiankang 建康 (modern-day Nanjing), the capital of the Eastern Jin dynasty 東晉 (317-420). In reality, the tilt is slightly more than 32 degrees, making the given value quite close to the actual measurement. Similarly, the statement "the North Pole is 115 degrees from the ecliptic, while the South Pole is 67 degrees from the ecliptic" allows to deduce the obliquity of the ecliptic at that time and shows that this value is quite accurate.
This demonstrates that Yu Song indeed possessed solid astronomical knowledge. However, since his theory overall still belonged to the Canopy-Heaven model, it did not have a significant impact on the course of astronomical history.