摘要
In pre-modern China,systematic records of astronomical phenomena measured by units including“zhang,”“chi,”and“cun”and records using phrases such as“as large as something”(making comparison with images取象比类)were kept.Some of these records survive and together they constitute a“scale system”for records of astronomical phenomena.A textual model of the celestial sphere based on naked eye observations also survives.According to this model and using the conversion ratio that 1 chi equals 1 degree,the author has reconstituted the geometric meaning of the records of“zhang,”“chi,”and“cun,”while records that use a comparison with a certain object have been converted to their apparent diameters or magnitudes.Finally,these two records are integrated into one system.Through an analysis of the origin of the chi system,the author obtains the result that the radius of the celestial sphere when the ancients observed the sky with the naked eye was about 13 meters.The paper supports this conclusion from various perspectives,including psychological factors,the radius of planetariums,and the nautical Method of Reckoning by the Stars.As naked eye observers always regard the vault of heaven as a plane hemisphere,they have a common false impression in their minds;the pre-modern observational data therefore contains some systematic errors.Under different illumination and weather conditions,the vault of heaven is plane in varying degrees,for which the author has defined“the angle of apparent plane degree”视扁度角.To correct the visual errors,the author has devised a series of calculation tables for daytime,nighttime,cloudy days,clear days,moonlit nights,and moonless nights,to convert the apparent heights or sizes of celestial bodies to the true heights or sizes.
古代以“丈、尺、寸”为单位的天象记录以及“大如某物”形式(取象比类)的记录是成系统的,可统称为古代天象记录的“尺度体系”。古人裸眼目视观测天象时亦有天球模型,通过天球模型的建立,按1尺=1度的换算标准,可以确定“丈、尺、寸”天象记录的几何意义,并对“大如某物”形式的记录进行尺度或亮度的量化,最后将两种记录统一在一个系统中。通过对尺寸系统起源的分析,作者认为古人裸眼目视观测时的天球半径约为13米。本文还从人本心理行为渊源、天文馆天象厅的半径、航海牵星术等多方面进行了论证。人裸眼目视观测天象时有共同的视错觉现象,形成系统误差,此误差是将天穹视为扁平状造成的。在不同的天空照度与气象条件下,其扁平程度有所不同,可引入“视扁度角”概念加以量化。为对视觉误差进行校正,作者求出了各种状况下(昼、夜、阴、晴、有月、无月)裸眼目视观测时天体视高度、视长度与其真实尺度的校正归算表。
