邢台学院学报

郭守敬在日影测量上的第一项突破，是对传统的立杆测影进行改进，即发明了“八尺圭表-景符日影测量系统”。结合系统论基本原理，认为郭守敬在日影测量的第二项突破，是“四丈高表-景符日影测量系统”。应用高等数学研究了“四丈高表-景符日影测量系统”本身的特征，给出了本影长度、影宽、相对精度、横梁影子对称性、光斑宽、光斑对称性、影宽/光斑宽、光斑右宽/光斑左宽等8个变量随太阳高度角的变化规律。应用该结果，得出三个结论：其一，郭守敬改进的“四丈高表-景符日影测量系统”,是又一个革命性的突破；其二，相对于“八尺圭表-景符日影测量系统”,新系统是一次成功日影测量数学模型的大型实验装置；其三，新系统为后期的《授时历》提供了坚实的仪器基础。

Guo Shoujing's first breakthrough in sun shadow measurements to improve the traditional 8-chi Gnomon shadow measurement, is the “8-chi gnomon-shadow definer sun shadow measurement system”. Based on the basic principles of system theory, this paper believes that Guo Shoujing's second breakthrough in the sun shadow measurement can be called the “4-zhang high gnomon-shadow definer sun shadow measurement system”. Further, advanced mathematics is applied to study the characteristics of the “4-zhang high gnomon-shadow definer sun shadow measurement system” itself, and the variation rules of eight variables with Solar zenith angle, including the length of the umbra, the width of the shadow, the relative precision, the symmetry of the beam shadow, the width of the light spot, the symmetry of the light spot, the width of the shadow/the width of the light spot, and the ratio of the length of right/left of the light spot. The application of the results shows that: “4-zhang high gnomon-shadow definer sun shadow measurement system” improved by Guo Shoujing is a new revolutionary breakthrough; compared to “8-chi gnomon-shadow definer sun shadow measurement system”, this new system is a large-scale experimental device for successfully measuring the mathematical model of solar shadow; the new system provides a solid instrument foundation for the later Shoushi Calendar.