晷影测年:以陶寺疑似圭尺为例

Observing the Year with a Sundial Shadow:The Painted Pole from Taosi as an Example

2002年山西襄汾陶寺城址出土一件残长171．8厘米，且有43个色段端点的漆木杆，疑似标注中天日影的圭尺。为此，文章构建了普适的仅由晷影数据（或刻度）求解圭表观测年代的模型。该模型功能较强，能将未知的表高、圭表间距及太阳位置、观测误差等参数同时解出，可广泛用于圭表测年问题。为求陶寺漆杆的观测年代，设定可允许的最大高度角误差为0.1°，设定表高80-250cm、圭表间距0-200cm，步长1cm；所求年代范围为BC2201-BC1901，步长0．001d。将这些参数和色段端点的数据代入模型处理，并考虑大气折射的影响，结果表明，色段端点中最少有67％与日影无关，故目前判断其为观测日影的圭尺尚存困难。

In 2002, the remains of a painted lacquer pole 171.8 cm long marked with 43 colored sections was unearthed at Taosi in Shanxi Province. It has been suggested that it was a ruler used to measure the shadow of the sun when in transit. For this reason this paper designs a universal model to solve the year only from the shadow data of the sun after meridian observation. The model is powerful, as it can be used to derive unknown parameters, such as the height of the pole, the length between the pole and ruler, and observation errors, and also can be widely used in sundial chronology problems. In order to obtain the observing year of this painted pole, we set 0.1 degree as the maximum allowed error of elevation, a height of 80-250 cm for the pole, 0-200 cm for the distance between the pole and the ruler, and steps of 1 cm. We then set the years for between 2201 BC to 1901 BC, its steps 0. 001 day, and put all the parameters and data of the 43 colored sections into the model, taking into consideration the influence of atmospheric refraction. Results indicating that at least 67% of the color sections have nothing to do with the shadows of the sun, cast doubt on the theory that the painted pole from Taosi was a ruler used to record the shadows of the sun.