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.
WANG Yumin (Wed,) studied this question.