中国历代日月交食周期的研究

中国自西汉至南宋共使用了２９个日月交食周期，如重复不计，实有２２个周期。计算交食周期的方程式通常有下列六式：（１）半食年／朔望月＝会月／会率，（２）半食年／回归年＝会岁／会率，（３）食年／朔望月＝会月／朔望合数（交率），（４）食年／回归年＝会岁／朔望合数（交率），（５）交点月／朔望月＝会月／交数，（６）食年／交点月＝交数／交率。中国古代以“大衍求一术”计算交食周期，与近代用连分数法算得的结果完全相同。经验算，绝大部分交食周期十分准确、密近。本文还对王充（甲）、（乙）、（丙）三周期以及中西交食周期的雷同进行了探讨。

RESEARCH ON THE PERIODICITY OF SOLAR (AND LUNAR) ECLIPSES USED IN CHINESE CALENDARS OF PAST DYNASTIES

In the about 1400 years from the Western Han Dynasty (206 B.C.-A.D. 24) to the Southern Song Dynasty(1127-1279), 29 periodicities of eclipese, or 22 periodicities with the omission of duplicates, had been used in China. The equations usually applied for seeking and calculating periodicities are as follows:The results of Qin Jiushao's method known as da yan qiu yi shu coincide completely with those obtained by using the modern method of continued fraction. This paper also discusses 3 periodicities of Wang Chong of the Eastern Han Dynasty (A.D. 25-220) as being identical with those used in Western civilizations.