A Study On The Calendar-time And Eclipse In The Song Dynasty

The calendar plays an extremely important role in Chinese traditional culture. This paper chooses the algorithms of new moon, intercalary months arrangement and eclipse in calendars of Song dynasty as the research object and the starting point. After all, this paper has a detailed interpretation of the algorithms of new moon, intercalary months arrangement and eclipse through literature analysis and mathematical formulations, and makes the accuracy of them by related computer programs to analyze the various error sources. The main part works as follows:1) Analyzed the time measurement and calculating in Song dynasty, it points out that a complete time system had been established in the Song dynasty. Combed the history of calendars in Song dynasty, it discusses the political background before and after each calendar reformed.2) The algorithms of new moon, intercalary months arrangement and eclipse of each calendar in Song dynasty has been interpreted in details. Compared with the reconstruction model, this paper analyzed astronomical significance and principle of various algorithms and constants. It points out that the algorithms of new moon, intercalary months arrangement and eclipse ignored some secondary factors, however, because it was considered as the most important factors, it is reasonable and partially correct. Real new moon algorithm, embolism algorithm and eclipse algorithm are expressed in modern mathematical formula, and comparatively analyzed. Especially, this paper has got the real new moon algorithm in "Yingtianli" and the eclipse algorithm in "Mingtianli". According to this, the evolutionary process of models of the algorithms of new moon, intercalary months arrangement and eclipse in Song dynasty has been established.3) The algorithms of new moon and intercalary months arrangement of the11calendars and the eclipse algorithms of "Chongtianli" and "Jiyuanli" have been compiled into computer software, which would have simulated and recovered any given years of the intercalary months and eclipse. Some important intermediate results such as the mean new moon, the rectified number of sun and moon and shicha can also be clearly visualized. The accuracy of the real new moon and eclipse of calendars in Song dynasty can be given in the way while contrasting the recovered results with the value of modern theory. The error in calculating real new moon is less than25minutes; the error of the middle of solar eclipse is about30minutes while magnitude of eclipse error is about1.5minutes; the error of the middle of lunar eclipse is about20minutes while magnitude of eclipse error is about1. The conclusion is drawn that the calculation of the real new moon is superior to the eclipse and the middle of eclipse is better than the magnitude of eclipse in prediction. The highest accuracy is "Kaixili" and the lowest is "Huiyuanli" in all calendars. However, according to the evaluation from the aspect of ancient view, the calendar accuracy is increasing continuously from Northern Song dynasty to the Southern. As to the eclipse algorithm accuracy, Jiyuanli is much better than Chongtianli.4) By analyzing error cycle, the mean new moon errors, rectified number of sun and moon errors and a comprehensive analysis of these various errors, the main influential factors and characters that impacts on the real new moon errors will be explored. The new moon error is characterized as strictly periodic, thus, the mean new moon error can be calculated. The maximum error of rectified number of sun and moon appears only when the sun and the moon run near perigee at the same time. Among the numerous factors influencing the real new moon, the rectified number of moon is the most significant factor."Jiyuanli", for example, based on the calculation for the accuracy of the real New Moon and eclipse, the average error of shicha can be obtained. The error of average absolute value of "Jiyuanli" shicha is about0.5hours and is bigger than the result of the reconstruction model. This paper points out that the ancient eclipse calculating process is a numerical algorithm system. Those middle processes that are correction of the mean new moon to the real new moon and shicha to the middle of the eclipse are designed for calculation of the final eclipse time. As long as the eclipse time calculate with high precision and reach a certain standard, it can be concluded that a set of numerical algorithm of eclipse is reasonable and excellent.5) By using the calculated results of the real new moon and eclipse, a primary comparison and analysis is made on the new moon, intercalary months and eclipse records in "SongShi" and "YuanShi". The result of the comparison is that a large part of records in "Songshilvlizhi" was calculated by the calendar don't conform to recovery results. Meanwhile, eclipse records in "Songshitianwenzhi" may be recorded according to the calculated results with the calendar at that time.