On the Achievements and Defects of Liu Xin’s Metrology Theory

GUAN Zeng-jian

School for History and Culture of Science, Shanghai Jiao Tong University

No 800, Dongchuan Road, Shanghai 200240, China

Liu Xin (刘歆) is a famous scientist in the history of Chinese science. In the Yuanshi (元始) years (A. D. 1~5) of West Han (西汉) Dynasty, he accepted Wang Mang’s appointment to organize a large-scaled reform of metrological systems then. One of the results of the reform was the formation of systematic theory of metrology. The theory had become the guidance of metrology of succeed dynasties since then. The other result of the reform was that under the guidance of Liu Xin’s metrology theory, a passel of standard apparatus of weights and measures have been designed and manufactured, which became models for later dynasties to produce their own standard apparatus of weights and measures.

Liu Xin’s theory of metrology developed on the basis of his understanding of numeral and temperament. About the cognition of numeral, he gave a definition of number at first and then described its social function and the relation between it and metrology. His ideas were clear and valuable to the development of metrology. But his further explanation of the function of figure leads his theory into digital mysticism at last.

Liu Xin’s theory of temperament is rich in contents. He described the social function of music and discussed the basic elements of music. He illustrated the connotation of 5 sounds, 8 voices and 12 temperaments as well as their relations to all nature things and social affairs. He explained his understanding of how temperaments coming from and what is the way of their formation. However, in order to make the way looks in uniform, he gave up the demand of temperament’s own quality, which caused a mistake in his theory of 12 temperaments producing each other.

The core of Liu Xin’s metrology theory is the theory of “uniting length, capacity and weight on the basis of temperaments by means of broomcorn millet(乐律累黍说)”. Such a theory established a kind of inner link between temperaments and metrology, which lead to a formal unity of the holiness of music and the preciseness of metrology at last. It also made the unification of length, measures, weight and temperaments became true in form. Therefore it at last became the most authoritative theory of metrology in the history of ancient China. However, the key of the theory that the length of Huangzhong tube is 9 Cun(寸) may cause mistakes in practice because that when a tube is used for standard pitch apparatus, it is necessary to make some amendment of the tube mouth, but Liu Xin’s theory did not refer to it at all.

In a word, Liu Xin’s metrology theory is very important in the history of Chinese metrology, it played a guiding rule to the development of ancient Chinese metrology. However, there were still some defects in his theories, which are seldom recognized by people today.