邢云路对《授时历》日躔过宫推步的改进

The Calculation of Shoushi Li When the Sun Transited Zodiacal Signs Improved by Xing Yunlu

考察明末邢云路所撰《古今律历考》中述及的日躔推步实例与先期恢复的《授时历》和《大统历》方法进行推步比对.采用邢云路改进的《授时历》法推步万历己亥岁(1599年)日躔交宫时间,结果与邢氏的标准偏差为5.93刻(=85.39 min),同时交宫夜半黄道宿度的偏差0.06古度(=0.059°);其中若扣除戌宫可能因数据错误产生的较大误差,则标准偏差将降为1.38刻(=19.87 min)和0.01古度(=0.0099°).其次,采用《大统历》计算该年日躔交宫,与邢云路计算的标准偏差为1.09刻(=15.70 min),交宫夜半黄道宿度的标准误差为0.05古度(=0.049°).据此可认为:基本恢复了邢氏的日躔推步方法;邢云路并未对《授时历》的日躔推步方法作本质上的改进,只是修改了其中的年长、周天分及宫界度.研究表明,邢氏所得《大统历》推交宫的结果与《授时历》偏差过大,原因在于其修改了《授时历》的参数,邢氏有厚《授时》薄《大统》之嫌.

The book Gujin Liilikao was written by Xing Yunlu, an ancient astronomer in the latter Ming dynasty. In this paper, base on our previous recovery for both calendars of Shoushi Li and Datong Li, we investigate the Xing＇s practical calculations for the times and locations when the sun transited zodiacal signs, then check and compare his results with our calculations after accepted Xing＇s parameters and the methods. First, when using the improving Shoushi methods claimed by Xing, we obtain, in the year of Wanli Jihai （1599）, the standard error of the time between our calculations and Xing＇s results when the sun transit each of the zodiacs is 5.93 Ke （=85.39 min）, but when ignore the biggest error derived by Zodiacs Xu, the error will decrease to 1.38 Ke （=19.87 min）, and at the same time the standard deviation of solar longitude at middle-night just before transit is 0.06 Du （=0.059° ）. The second, when employing our recovering methods of Datong Li and comparing with Xing＇s calculation, we ascertain that in the same year the standard error of the time when the sun transit each of the zodiacs is 1.09 Ke （=15.70 min）, and the standard error of solar longitude at middle-night just before transit is 0.005 Du （=0.049° ）. So we are sure we have recovered the work declared byXing. And in fact Xing do not improve the method of Shoushi Li but provide the new values of the tropical year-length, the data of Zhoutian Fen （the degrees of the whole ecliptic or celestial equator）, and the range of each zodiac. At the same time, the bigger deviations between both calendars derived by Xing just caused by his new parameters, and this probably leads to Xing approving Shoushi Li and despising Datong Li.