Gnomon shadow lengths recorded in the Zhoubi Suanjing: The earliest meridian observations in China?

Abstract

The Zhoubi Suanjing, one of the most important ancient Chinese books on mathematical astronomy, was compiled about 100 BC in the Western Han dynasty (BC 206 - AD 23). We study the gnomon shadow lengths for the 24 solar terms as recorded in the book. Special attention is paid to the so-called law of cun qian li, which says the shadow length of a gnomon of 8 chi (about 1.96 m) high will increase (or decrease) 1 cun (1/10 chi) for every 1000 li (roughly 400 km) the gnomon moves northward (or southward). From these data, one can derive the time and location of the observations. The results, however, do not fit historical facts. We suggest that compilers of the Zhoubi Suanjing must have modified the original data according to the law of cun qian li. Through reversing the situation, we recovered the original data, our analysis of which reveals the best possible observation time as 564 BC and the location of observation as 35.78° N latitude. We conclude that this must be the earliest records of solar meridian observations in China. In the meantime, we give the errors of solar altitudes for the 24 solar terms. The average deviation is 5.22°, and the mean absolute deviation is 5.52°, signifying the accuracy of astronomical calculations from that time. © 2009 National Astronomical Observatories of Chinese Academy of Sciences and IOP Publishing Ltd.