On the Function of the Warring States Chu “Royal” Bronze Beams as Well as “Establishing it with Things” in Lu Jiuci Asked Chen Qi about Numbers

Abstract

<p>The National Museum of China houses two bronze balance beams inscribed with the character “wang (王, king or royal)” reportedly unearthed in Shou County, Anhui Province. These artifacts are undoubtedly from the Warring States period state of Chu. Given the presence of scales on the beams, scholars generally believe these items represent an intermediate stage in the development from balance scales to steelyards, making them a transitional type of weighing instrument. However, the exact function of these bronze beams remains somewhat unclear. This article attempts to propose a new hypothesis by integrating mathematical data from texts on excavated bamboo slips. It suggests that the “royal” bronze beams were not used for the accumulation of standard weights but rather for the division of unit weights, corresponding to the terms “destroy” (hui毁) or “break” (po破) mentioned in unearthed arithmetic books. This function might have two specific applications: first, to establish or verify standard weights, and second, to achieve more precise measurements when the smallest standard weight was still not accurate enough. Based on this, the article will also reconsider the phrase “yi wu qi zhi” (以物起之, establishing it with things) from the Peking University Qin manuscript Lu Jiuci Asked Chen Qi about Numbers (Lu Jiuci wenshu yu Chen Qi 鲁久次问数于陈起), suggesting that it discusses the relationship between measurements and fractions.</p>

中国国家博物馆藏有两件带有“王”字刻文的战国楚铜衡杆。 由于衡杆上带有刻度，学界通常认为两器标志着由天平向杆秤发展的中间阶段，是一种过渡型的衡器。 至于铜衡的具体用法，目前的认识还比较模糊，并且存在共时和历时两个方面的疑点。 本文试图结合简牍数学资料对此提出新的假说，即它们并不依赖单位砝码重量的叠加，而是用于单位重量的分割，即出土算数书中所谓的“毁”或者“破”。 这一功能可能有两种具体的应用方式，一是用于确立或者检验砝码的重量，二是在最小单位砝码依然精度不足的情况下，进行更加精确的测量。 在此基础上，本文还将重新思考北大秦简《鲁久次问数于陈起》篇中的“以物起之”一句，认为其所讨论的对象是度量衡与分数的关系。