The "Rites of Zhou" states: "The Li family was tasked with creating standard measuring vessels known as 'lè.' It is one foot deep, with an inner square measuring one foot on each side and an outer circular shape, with a volume of one lè. Its small opening (tū) has a diameter of one inch and a volume of one dǒu; its large opening (ěr) has a diameter of three inches and a volume of one shēng. A lè weighing one jūn produces a sound that resonates at the same pitch as the yellow bell. This measuring vessel is exempt from tax. Inscribed on it are the words: 'Designed with care, aiming for perfection; standard measuring vessels have been established for reference by the four nations; to be followed by future generations, this vessel serves as the criterion.'" This passage mainly discusses the manufacturing standards and specifications of an ancient standard unit of volume called "lè."
The "Zuo Zhuan" of the "Spring and Autumn Annals" records: "In the state of Qi, there were four types of volume units: dǒu, qū, lè, and zhōng. Four shēng make one dǒu, four dǒu make one qū, four qū make one fǔ, and ten fǔ make one zhōng." One qū equals six shēng, one fǔ equals six dǒu and four shēng, and one zhōng equals sixty-four dǒu. Zheng Xuan posits that the fǔ is shaped like a square with sides measuring one foot, with a volume of one thousand cubic inches, which slightly differs from the calculation in "Nine Chapters on the Mathematical Art: Grain," being short by two shēng and eighty-one twenty-second parts. After calculations, the volume of the ancient hǔ is approximately one thousand five hundred sixty-two point five cubic inches, shaped with a square base and a circular body, one foot deep, and with a diameter of about one foot four inches, one-tenth, four hao, seven seconds, and two hu.
In "Nine Chapters on the Mathematical Art: The Work of Commerce," it is stated that a hu of millet has a volume of 2700 cubic inches; a hu of rice has a volume of 1627 cubic inches; and a hu of beans, peas, sesame, and wheat has a volume of 2430 cubic inches. This indicates that ancient people established different volumes based on the weight of grains in order to ensure consistent prices, rather than making all grains the same volume. Using the hu of rice as a standard yields results similar to those recorded in the "Book of Han." In the fourth year of the Wei Jingyuan era, when Liu Hui provided commentary on "Nine Chapters on the Mathematical Art: The Work of Commerce," he said: "The hu currently used by the Grand Minister of Agriculture has a circumference diameter of one foot three inches five fen five hao, a depth of one foot, and a volume of 1441 inches plus three fen. The copper hu from the time of Wang Mang, calculated according to today's ruler, has a depth of nine inches five fen five hao, a circumference diameter of one foot three inches six fen eight hao seven mao. According to my calculation method, the volume of Wang Mang's hu is slightly over nine dou, seven sheng, and four he." This shows that the hu during the Wei Dynasty was relatively large, and the ruler was also relatively long; while the hu of the Wang Mang era was comparatively smaller, and the ruler was also relatively short. This passage primarily discusses the units of capacity and volume calculations for various grains across different periods, as well as the differences in measuring instruments in different periods. As for this "hengquan," the term "heng" refers to balance, while "quan" refers to weight. The purpose of the balance is to support weight and achieve equilibrium among objects, that is, to distinguish between light and heavy. Ancient balances went by many names, such as shu, lei, chui, zi, huan, jun, lue, yi, etc., and the names and standards of each dynasty differed. The "Book of Han" records that the names and principles of the balance system of the Han Dynasty were explained very clearly, but it underwent numerous changes over time, and how it was specifically changed is unknown. During the Yuan Kang era, Pei Wei believed that medical prescriptions were critical to people's lives, but at that time, the weight units for measurement were different from ancient times, resulting in significant consequences. Therefore, he suggested reorganizing the balance system; however, his suggestion was ultimately disregarded.
In the eighteenth year of Zhao Shile's reign, in July, when the Jiande Hall was being built, a round stone was discovered, resembling a water millstone, inscribed with: "Standard Stone, weighing four jun, for measuring weights and measures. Made by the Xin family." After some discussion, it was concluded that this stone dates back to the time of Wang Mang. This stone, also weighing four jun, bore the same inscription "for measuring weights and measures," indicating that it served as a standard for weight calibration, produced by the Xin family during the Wang Mang era.
