¹ Yang, Liu, “Objects from the Qin Dynasty,” in China's Terracotta Warriors: The First Emperor's Legacy, edited by Yang, Liu et al. (Minneapolis: Minneapolis Institute of Arts, 2012), 229–95Google Scholar; Pines, Yuri et al. , eds., Birth of An Empire: The State of Qin Revisited (Berkeley: University of California Press, 2014)Google Scholar; Sanft, Charles, Communication and Cooperation in Early Imperial China: Publicizing the Qin Dynasty (Albany: State University of New York Press, 2014)Google Scholar.

² For the original version and translation, see Charles Sanft, Communication and Cooperation, 59–60. See also Loewe, Michael, Problems of Han Administration: Ancestral Rites, Weights and Measures, and the Means of Protest (Leiden: Brill, 2016), 180–84CrossRefGoogle Scholar.

³ For the studies of measurement systems in ancient Mesopotamia, see Robson, Eleanor, Mathematics in Ancient Iraq: A Social History (Princeton: Princeton University Press, 2008), 115–23Google Scholar; Ascalone, E. and Peyronel, L., “Two Weights from Temple N at Tell Mardikh-Ebla, Syria: A Link between Metrology and Cultic Activities in the Second Millennium BC?” Journal of Cuneiform Studies, 53.1 (2001), 1–12CrossRefGoogle Scholar; M. A. Powell, “Ancient Mesopotamian Weight Metrology: Methods, Problems and Perspectives,” in Studies in Honor of Tom B. Jones (Alter Orient und Altes Testament 203), edited by M.A. Powell and R.H. Sack (Kevelaer/Neukirchener-Vluyn: Butzon & Bercker/Neukirchener, 1979), 71–109. For modern Europe, see Terry Quinn, From Artefacts to Atoms: The BIPM and the Search for Ultimate Measurement Standards (New York: Oxford University Press, 2012); Alder, Ken, The Measure of All Things: The Seven-Year Odyssey that Transformed the World (London: Abacus, 2002)Google Scholar. But these sources, similar to those of Chinese historians, focus on the measurement systems, but not on the actual designing and production of the measures.

⁴ Qiu Guangming 丘光明, “Shilun Zhanguo hengzhi” 試論戰國衡制, in Zhongguo gudai duliangheng lunwenji 中國古代度量衡論文集, edited by Henan Sheng Jiliangju 河南省計量局 (Zhengzhou: Zhongzhou Guji, 1990), 382–403; Qiu Guangming et al., Zhongguo kexue jishu shi: duliangheng juan 中國科學技術史：度量衡卷 (Beijing: Kexue, 2001); Michael Loewe, Problems of Han Administration.

⁵ Qiu Guangming et al., Zhongguo kexue jishu shi, 180, chart no. 10-3. There were probably containers made of organic materials, such as wood, as well; but they have likely all decayed.

⁶ Ma Chengyuan 馬承源, “Shang Yang fangsheng he Zhanguo liangzhi” 商鞅方升和戰國量制,” in Zhongguo gudai duliangheng lunwenji 中國古代度量衡論文集, 254–60; Qiu Guangming, “Shilun Zhanguo hengzhi;” Tang Lan 唐蘭, “Shang Yang liang yu Shang Yang liangchi” 商鞅量與商鞅量尺, in Zhongguo gudai duliangheng lunwenji, 56–63; Qiu Guangming et al., Zhongguo kexue jishu shi, 166–69, 178–85; Loewe, Problems of Han Administration, 180.

⁷ Qiu Guangming et al., Zhongguo kexue jishu shi, 167, chart no. 9-19, item no. 4, and 168.

⁸ Accession number (no.) in the Shanghai Museum collection, 44331. See Guojia Jiliang Zongju 國家計量總局 et al., Zhongguo gudai duliangheng tuji 中國古代度量衡圖集 (Beijing: Wenwu, 1984), 44; Qiu Guangming et al., Zhongguo kexue jishu shi, 166–68. See also Chen Peifen 陳佩芬, Xia Shang Zhou qingtongqi yanjiu 夏商周青銅器研究, vol. 6 (Shanghai: Shanghai Guji, 2004), 470–73, no. 641. I call objects of this type “containers” in this article, as they include capacity measures and other objects that bear similar shapes but did not really serve as standard measures.

⁹ For an account of the life of Shang Yang, see Pines, Yuri, The Book of Lord Shang: Apologetics of State Power in Early China (New York: Columbia University Press, 2017), 7–24Google Scholar. Translation of the title Daliangzao 大良造 is based on the translation of Dashangzao 大上造 in Anthony J. Barbieri-Low and Robin D.S. Yates, Law, State, and Society in Early Imperial China: A Study with Critical Edition and Translation of the Legal Texts from Zhangjiashan Tomb no. 247 (Leiden: Brill, 2015), vol. 1, xxii, section 1.5, “Early-Han Orders of Rank Mentioned in the Zhangjiashan Legal Texts.”

¹⁰ Qiu Guangming et al., Zhongguo kexue jishu shi, 166–68; Chen Peifen, Xia Shang Zhou qingtongqi yanjiu, vol. 6, 471.

¹¹ Qiu Guangming, “Shilun Zhanguo hengzhi;” Tang Lan, “Shang Yang liang yu Shang Yang liangchi;” Ma Chengyuan, “Shang Yang fangsheng he Zhanguo liangzhi.”

¹² 202 cubic cm/16.2 cubic Qin cun = 12.48 cubic cm (1 cubic Qin cun = 12.48 cubic cm; 1 Qin cun = 2.32 cm; 1 Qin chi = 10 Qin cun; thus 1 Qin chi = 23.2 cm).

¹³ This inscription translates literally as “the city of Xianyang, one dou and three sheng.”

¹⁴ Qiu Guangming et al., Zhongguo kexue jishu shi, 167, chart no. 9-19, item no. 4, and 168.

¹⁵ Original version and translation from Sanft, Communication and Cooperation, 59–60. See also Li, Kin Sum (Sammy), “To Rule by Manufacture: Measurement Regulation and Metal Weight Production in the Qin Empire,” T'oung Pao 103.1–3 (2017), 30–32CrossRefGoogle Scholar.

¹⁶ See the study of the production and design of metal weights in Li, “To Rule by Manufacture,” 1–32; and Kin Sum (Sammy) Li, “The Design Origins of Qin Metal Weights,” Artibus Asiae 77.1 (2017), 91–110. Li, “To Rule by Manufacture,” addresses the importance of studying the relationship between the governance of the empire and the production of the metal weights. I hypothesize there that weight production methods were determined by the government's political agenda, which was concerned with communicating its regulation policy to its subordinates. See also Sanft, Communication and Cooperation. “The Design Origins of Qin Metal Weights,” discusses the origins and development of the designs of the metal weights. The Qin weight designers seem to have deliberately controlled the appearance of the weights and demonstrated no attempts to create completely innovative designs.

¹⁷ Sanft, Communication and Cooperation, 72–73.

¹⁸ See Bagley, Robert, “Anyang Mold-making and the Decorated Model,” Artibus Asiae 1 (2009), 39–90Google Scholar; , Bagley, “Shang Ritual Bronzes: Casting Technique and Vessel Design,” Archives of Asian Art, 43 (1990), 6–20Google Scholar; Kerr, Rose and Wood, Nigel, Science and Civilisation in China, vol. 5: Chemistry and Chemical Technology, part XII: Ceramic Technology (Cambridge: Cambridge University, 2004), 399–407Google Scholar.

¹⁹ The inscription on the Qin bronze weights was usually cast and not engraved. See Li, “To Rule by Manufacture,” 22.

²⁰ Chen Peifen, Xia Shang Zhou qingtongqi yanjiu, vol. 6, 471–73.

²¹ For the translation of the edict, see Sanft, Communication and Cooperation, 59.

²² Name of a county, in today's Shaanxi Pucheng 陝西蒲城. See Chen Peifen, Xia Shang Zhou qingtongqi yanjiu, vol. 6, 471.

²³ In today's Shanxi Linxian 山西臨縣. See Chen Peifen, Xia Shang Zhou qingtongqi yanjiu, vol. 6, 471.

²⁴ Chen Peifen, Xia Shang Zhou qingtongqi yanjiu, vol. 6, 471. Qiu Guangming and his colleagues mention that Li Xueqin 李學勤 argued that the fifth character should not be read as “shuai” 率. But Qiu Guangming and his colleagues do not give any reason to support this reading. See Qiu Guangming et al., Zhongguo kexue jishu shi, 166n1. I follow Wang Hui's decipherment in Wang Hui 王輝, “Pinli de qiyuan jiqi yanbian” 聘禮的起源及其演變, Qin Shihuang Diling Bowuyuan 秦始皇帝陵博物院 (2012), 418; he reads the fifth character as “qian” 遣.

²⁵ See Li, “To Rule by Manufacture,” 6; Zhongguo gudai duliangheng tuji, 126, no. 180.

²⁶ Ma Chengyuan, “Jinhou Su bianzhong” 晉侯穌編鐘, in Jinhou Mudi Chutu Qingtongqi Guoji Xueshu Yantaohui lunwenji 晉侯墓地出土青銅器國際學術研討會論文集, edited by Shanghai Bowuguan 上海博物館 (Shanghai: Shanghai Shuhua, 2002), 9. An earlier version of this article appears in Shanghai Bowuguan jikan 上海博物館集刊, vol. 7, edited by Shanghai Bowuguan jikan Bianji Weiyuanhui 《上海博物館集刊》編輯委員會 (Shanghai: Shanghai Shuhua, 1996), 1–17; see also Guan Xiaowu 關曉武 et al., “Jinhou Su zhong keming chengyin shitan” 晉侯穌鐘刻銘成因試探, in Jinhou Mudi Chutu Qingtongqi Guoji Xueshu Yantaohui lunwenji, 331–45.

²⁷ See Ma Chengyuan, “Jinhou Su bianzhong,” 9.

²⁸ See Chen Peifen, Xia Shang Zhou qingtongqi yanjiu, vol. 6, 471.

²⁹ Bagley, “Anyang Mold-making and the Decorated Model,” 39–90.

³⁰ See Kerr and Wood, Ceramic Technology, 401–2.

³¹ Li, “To Rule by Manufacture,” 22.

³² See www.makifit.com/bmbw/detail2.html. By 3D scanning of artefacts and making these scans available online, a new approach to the study of art history and archaeology has been invented. Readers’ perspectives are limited when viewing 2D images and they cannot either re-examine or validate the original observer's results. But 3D models allow full access to the real dimensions of the artefacts. Scholars can use this tool to validate the original observer's conclusions by repeating the observation process the observer is recorded to have followed and developing their own perspectives as they examine the artefacts in a new light.

³³ The accession no. of the other container, which is also in the Shanghai Museum collection, is 46425.

³⁴ Qiu Guangming et al., Zhongguo kexue jishu shi, 166–68, 179; Chen Peifen, Xia Shang Zhou qingtongqi yanjiu, vol. 6, 473. Even though the measuring staff stated that they performed the most scientific measuring of the two containers, variations and errors may still exist because different people may have chosen different points to measure. The two containers were not made to modern standards. Therefore, statistical variations are to be tolerated. See Liu Yanfei 劉艷菲 et al., “Shandong Zoucheng Zhuguo gucheng yizhi xinchu taoliang yu liangzhi chulun” 山東鄒城邾國故城遺址新出陶量與量制初論, Kaogu 考古 2019.2, 101n4. They used millet grain to measure the volumes of pottery containers. But measurements at different times also differ. For example, the volume of one of the pottery containers they measured, H404②:18, ranges from 3622 to 3773 ml. See Liu Yanfei et al., “Shandong Zoucheng Zhuguo,” 90. They conclude that deformation and restoration of the pottery containers on the one hand, and measurements by different persons at various times on the other hand, are the likely factors leading to these variations. There is one more cuboidal container for comparison. See Zhongguo gudai duliangheng tuji, 59, no. 99. It was previously housed in the Zhongguo Lishi Bowuguan 中國歷史博物館, which is now called “the National Museum of China.” But the National Museum of China did not reply to my request for access to this container. It is recorded that the length of the entire object is also 18.7 cm and its volume is 210 ml. But the dimensions of its rectangular cavity are different: 14.5 x 8.4 x 2.6 (= 316.68) cm³. A part of the measurement record must be wrong.

³⁵ The software used is Meshlab (www.meshlab.net/) and 3D Reshaper (www.3dreshaper.com/fr/).

³⁶ I have been unable to locate any spacer, which would be used to stabilize the distance between the core and outer mold sections, on the two containers. Perhaps the Qin casters did not use a spacer, and instead had some other techniques to stabilize the distance; or alternatively the spacers are covered by corrosion.

³⁷ Liu Yu 劉煜 et al., “Yinxu chutu qingtong liqi zhuxing de zhizuo gongyi” 殷墟出土青銅禮器鑄型的製作工藝, Kaogu 考古, 2008.12, 85–6; Yue Zhanwei 岳占偉 et al., “Yinxu taofan, taomo, nixin de cailiao laiyuan yu chuli” 殷墟陶範、陶模、泥芯的材料來源與處理, Nanfang wenwu 南方文物, 2015.4, 158–59; Yue Zhanwei et al., “Yinxu taomo, taofan, nixin de zhizuo gongyi yanjiu” 殷墟陶模、陶範、泥芯的製作工藝研究, Nanfang wenwu, 2016.2, 137–40. On the contrary, Rose Kerr and Nigel Wood think that cores needed only to be pressed tight, but not to be fired. See Kerr and Wood, Ceramic Technology, 401–2.

³⁸ Zhongguo gudai duliangheng tuji, 41, no. 78.

³⁹ The measurers use the Chinese character “jing” 徑, referring to the circular mouths, bellies, and ring feet of the Zi Hezi and Chen Chun bronze containers. I take it as referring to their zhijing 直徑 (diameter).

⁴⁰ Photo by the author. See also Zhongguo gudai duliangheng tuji, 42, no. 79.

⁴¹ Zhongguo gudai duliangheng tuji, 55, no. 93.

⁴² Zhongguo gudai duliangheng tuji, 56, no. 94.

⁴³ Zhongguo gudai duliangheng tuji, 56, no. 95.

⁴⁴ Zhongguo gudai duliangheng tuji, 47, no. 84.

⁴⁵ Zhongguo gudai duliangheng tuji, 48, no. 85.

⁴⁶ Zhongguo gudai duliangheng tuji, 44, no. 81.

⁴⁷ Zhongguo gudai duliangheng tuji, 58, no. 98.

⁴⁸ Zhongguo gudai duliangheng tuji, 60, no. 100.

⁴⁹ Zhongguo gudai duliangheng tuji, 61, no. 101.

⁵⁰ Photo courtesy of the Tianjin Museum. Zhongguo gudai duliangheng tuji, 62, no. 102.

⁵¹ Zhongguo gudai duliangheng tuji, 63, no. 104.

⁵² Photo by the author. Zhongguo gudai duliangheng tuji, 64, no. 105.

⁵³ Zhongguo gudai duliangheng tuji, 66, no. 107.

⁵⁴ Zhongguo gudai duliangheng tuji, 67, no. 108.

⁵⁵ Zhongguo gudai duliangheng tuji, 68, no. 109.

⁵⁶ Zhongguo gudai duliangheng tuji, 69, no. 110.

⁵⁷ Zhongguo gudai duliangheng tuji, 70, no. 111.

⁵⁸ Cf. Bagley, “Anyang Mold-making and the Decorated Model,” 39–90. But mold lines could have been removed by polishing and may thus not be detectable on every container.

⁵⁹ I do not focus on the forms of production control in this article. For a discussion of this issue, see Li, “To Rule by Manufacture.” Since we do not have enough examples of archaeologically excavated Qin bronze containers, it is relatively difficult to reach a definite answer.

⁶⁰ Qiu Guangming et al., Zhongguo kexue jishu shi, 183.

⁶¹ Qiu Guangming et al., Zhongguo kexue jishu shi, 183.

⁶² It is stated in the catalogue that the inscriptions on the Zouxian ceramic containers were stamped. See Zhongguo gudai duliangheng tuji, 68–71. In order to determine whether the Zouxian containers might have been produced by the same workshop, we would want to check whether the stamped characters on one container are identical to the corresponding characters on another container. This would entail the application of 3D scan and display technology, because the container walls on which the inscriptions were stamped are curved. We can flatten the 3D models of the inscriptions and superimpose one upon another to determine whether they are in fact identical. Freely moving and rotating the 3D models enable us to compare carefully without being restrained by any museum regulations.

⁶³ See Liu Yanfei et al., “Shandong Zoucheng Zhuguo,” 89–104.

⁶⁴ Li, “The Design Origins.”

⁶⁵ See Tavernor, Robert, Smoot's Ear: The Measure of Humanity (New Haven: Yale University Press, 2007)CrossRefGoogle Scholar; Winchester, Simon, The Perfectionists: How Precision Engineers Created the Modern World (New York: Harper, 2018)Google Scholar; Robson, Mathematics in Ancient Iraq.

⁶⁶ Nelson, Robert A., SI: The International System of Units (Stony Brook: American Association of Physics Teachers, 1982)Google Scholar; Assendelft, O.W. Van, “The International System of Units (SI) in Historical Perspective,” American Journal of Public Health 77.11 (1987), 1400–1403CrossRefGoogle Scholar, www.ncbi.nlm.nih.gov/pmc/articles/PMC1647091/; Alder, The Measure of All Things; Quinn, From Artefacts to Atoms; Bureau International des Poids et Mesures, The International System of Units (SI), 8th edition (Paris: Organisation intergouvernementale de la Convention du Mètre, 2006), updated in 2014, English version, 93–180, retrieved on September 10, 2018 from www.bipm.org/utils/common/pdf/si_brochure_8.pdf; Isakov, Edmund, International System of Units (SI): How the World Measures Almost Everything, and the People Who Made It Possible (New York: Industrial Press, 2014)Google Scholar.

⁶⁷ See Bevan, Andrew et al. , “Computer Vision, Archaeological Classification and China's Terracotta Warriors,” Journal of Archaeological Science 49 (2014), 249–54CrossRefGoogle Scholar.