《大衍曆》日食原理

A Study on the Theory of Solar Eclipse in the 'Dayan Li'

一行在《大衍曆》（724年）中設計的日食算法，是張子信發現月亮視差對日食影響之後日食算法的一次全面改革，考慮了視食甚時刻太陽黃經、日月相對位置以及地理緯度等因素對日食預報的影響。通過對《大衍曆》術文的解讀，指出其蝕差算法相當於太陽時角h為0時（正午）的理論食差算法，由此得出結論：《大衍曆》蝕差算法為徐昂在《宣明曆》（822年）中提出日食三差算法模型提供了重要的舖墊和正確的思路，在中國傳統數理天文學日食理論的進化史上，占有承前啟後的重要地位。在此基礎上，搞清楚了《大衍曆》日食食限與食分算法的構造方法，並給出了九服蝕差算法的幾何解釋。

In his Dayan li (724 AD), Yi-xing designed a new algorithm for calculating articles related with the solar eclipse, which is a full-scale reformation after Zhang Zixin discovered the influence of solar eclipse computations caused by the lunar parallax. In his calendar, Yi-xing considered modifying factors such as the longitude of the sun, the relative position between the sun and the moon at the middle of solar eclipse, and the latitude at the place of the observer. On the basis of reading and analyzing original texts of the Dayan li, this article discusses the method how to construct the algorithm for judging when the solar eclipse will happen and for calculating the magnitude of the solar eclipse. The algorithm for calculating the deviation caused by the lunar parallax at the middle time of the solar eclipse in different places, namely Jinfu Shicha, is explained by a view of a geometrical angle. The Shicha algorithm shows that it was equivalent to a theoretical model when the hour angle of the sun h=0. These characteristics of algorithms can offer a correct interpretation of the shicha algorithm after Yi-xing.