The method of measuring shadows is plain: set up a gnomon on level ground and see how long its shadow is at noon. The length of the shadow changes with the season, and if it is measured accurately, the dates of the solar terms and the length of the year can be worked out.
In the Kaiyuan reign of the Tang, Yi Xing directed a nationwide survey of shadows and set a gnomon at Yangcheng (today's Gaocheng in Dengfeng), leaving the Duke of Zhou's shadow-measuring stand that survives today.
In 1276 (Zhiyuan 13 of the Yuan), Guo Shoujing and Wang Xun built the Dengfeng Observatory, using a tall gnomon to measure the length of the tropical year precisely.
The Shoushi calendar, issued in 1281, drew on observations that included those at Dengfeng and fixed the tropical year at 365.2425 days, from which the solar terms were set and the time was given to the people.
Dengfeng Observatory is the class in the chapter on Infrastructure on astronomical observation, centred on the Dengfeng Observatory: in the Tang, Yi Xing set up a gnomon at Yangcheng and measured its shadow; in the Yuan, Guo Shoujing and Wang Xun built the observatory and used a tall gnomon to measure the length of the tropical year, giving the Shoushi calendar a basis for fixing the solar terms and giving the time to the people.
