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題名 | 關於中國古代至日時刻測算法及其精度研究=A Study on the Method for Determining the Time of the Solstices in Ancient China and It's Precision |
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作者 | 王榮彬; Wang, Rong-bin; |
期刊 | 清華學報 |
出版日期 | 19951200 |
卷期 | 25:4 1995.12[民84.12] |
頁次 | 頁309-323 |
分類號 | 327.3 |
語文 | chi |
關鍵詞 | 中國古代曆法; 授時曆; 冬至; Ancient chinese calendars; Shoushi calendar; Winter solstice; |
中文摘要 | 在中國古代天文學史上,祖沖之(A.D.429-500)最先給出具有較嚴格數學意義的 冬至時刻測算方法。其方法建立在「二至前後影長變化是對稱的,且一日內影長變化是均勻 的」這樣的假定條件之上。本文對此方法及其數學表達式的原理作進一步的剖析。通過對比 分析古代測算值與現代理論計算值得出:雖然祖沖之算法公式的假設前提-一般地說是不成 立的,但在古代實際運用此方法的年代,它的誤差很小,其算法是可靠的;除假設條件外, 決定該算法精度的關鍵因素就是測影的精度。並發現測算公式的誤差隨著所用晷影組離至日 的時距增大而單調減小,且在離冬至45日左右取得最佳值。 通過進一步分析《授時曆》的二至時刻測算數據,認為該曆二至時刻的「曆取值」可能 採取了求平均值並四捨五入的原則。《授時曆》夏至時刻的誤差遠大於冬至,其原因可能是 由於古曆二至時刻測算的中心在冬至,夏至則冬至加減半個回歸年而得。《授時曆》作者通 過提高測影的精度,提出先進的數據處理方法,從而對提高冬至測算精度作出了貢獻。 |
英文摘要 | Zu, Chongzhi (A.D. 429-500), a celebrated mathematician and astronomer in Southern & Northern Dynasties, invented a relatively strict mathematical method for determining the time of the solstices first in the history of astron- omy in ancient China. The method was based on two hypothetical conditions:1) the change of the solar shade length is symmetrical with the solstices as its symmetric centre. 2)the change of the solar shade length in a day is uniform. This study analyses the mathematical fundamentals of the method and it is showed in this paper that the main errors of Zu's formula are due to the solar shade length's error and the formula's hypothetical sconditions. It is also showed that the errors of the hypothetical conditions are very small and the method was reliable in the years of the method was used. It is found that the crror of Zu's formula decreases as the time between the date of the set of solar shades and the winter solstice increases. The data analysis to the solstices of the Shoushi calendar shows that the writer of the calendar possibly adopted the principle of counting fractions over 1/2 as 1 adn disregarding the rest on the basis of average value. This study also discusses why the errors of summer solstices are much greater than those of the winter solstices in the Shoushi calendar, and points out that the method for determining the time of solstices is only practical for the winter solstice, the summer solstice is subordinately determined by the winter solstice and the length of tropical year in ancient Chinese calendars. The authors of the Shoushi calendar invented new instruments for measuring the solar shade and used an advanced data handling method so that they made a great contribution to improve the precision of the winter solstices but not to the formula of the calculation. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。