Wushen lichun kaozheng 戊申立春考證

Wushen lichun kaozheng 戊申立春考證 is a text on calendrical calculations written during the Ming period 明 (1368-1644) by Xing Yunlu 邢雲路, courtesy name Shideng 士登, from Ansu 安肅 (today's Xushui 徐水, Hebei). He obtained the jinshi degree in 1580 and was district magistrate of Fanshi 繁峙, Jixian 汲縣 and Linfen 臨汾, and then department secretary in the Ministry of War (bingbu zhushi 兵部主事), assistant administration commissioner (qianshi 僉事, canyi fushi 參議副使) in Henan and other places, and finally vice provincial administration commissioner (anchasi fushi 按察司副使) of Shaanxi.

In 1595, Xing observed discrepancies between the Datong Calendar 大統曆 and actual astronomical phenomena. He and Zhu Zaiyu 朱載堉 (1536-c. 1610) each submitted memorials requesting a calendar reform and presented their respective new calendar systems, though neither was adopted. In 1610, Xing was summoned to Beijing to participate in discussions on calendar reform. In 1616, he presented the book Qizheng zhenshu 七政真數 "The true data of the seven celestial bodies" (now lost), which detailed methods of astronomical calculations. In 1621, Xing identified shortcomings in the Shoushi Calendar 授時曆 by analyzing historical records of solar and lunar eclipses.

While serving as in Shaanxi, Xing Yunlu erected a gauge pillar (guibiao 圭表) in Lanzhou 蘭州 that stood six zhang tall—two zhang higher than the four-zhang pillar set up by Guo Shoujing 郭守敬, making it the tallest such instrument in ancient China. He conducted precise astronomical measurements over a 45-day period around the winter solstice, before the year 1608. His observations showed that the calculated time of the solar term lichun 立春 (the beginning of spring) differed from the predictions made by the Directorate of Astronomy (qintianjian 欽天監), which had calculated lichun to fall on the 21st day of the 12th lunar month at midnight (double-hour zi 子), while Xing Yunlu's calculations placed it on the 20th day of the 12th lunar month at high noon (hai 亥). Xing Yunlu analysed the reasons for this discrepancy and concluded that although the Datong Calendar was largely based on the Shoushi Calendar, it had omitted all corrections for precession (sui cha 歲差), leading to increasingly inaccurate predictions over time. This discrepancy led him to author an essay on the problem. The book of one fascicle was finished in 1608.

The most remarkable achievement of this book is Xing Yunlu's newly measured value for the true length of the tropical year (suishi 歲實): 365 days, 24 ke (quarters of an hour), 21 fen (minutes), and 90 miao (seconds), which, converted to modern notation, is 365.242190 days. Compared to the modern theoretical value, his calculation had an annual error of only 2.3 seconds, making it the most precise measurement not only of his time but in the entire history of ancient Chinese astronomy. Furthermore, when compared to the Western value in use at the time (365.2425 days), Xing Yunlu's calculation was significantly more accurate.

The text is included in the series Guang baichuan xuehai 廣百川學海 and Congshu jicheng chubian 叢書集成初編.