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WHY MILITARY INSTITUTIONS MATTER FOR CHINESE HISTORY CIRCA 600–1800

Published online by Cambridge University Press:  12 July 2017

David Robinson*
Affiliation:
Colgate University, e-mail: [email protected]
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Extract

This special issue of Journal of Chinese History makes the case that military institutions are essential for understanding Chinese history. Our goal is to engage a broad audience instead of talking exclusively to specialists in military history. Thus, rather than an institutional account of, say, the imperial guard, or detailed campaign narratives, readers will find here exploration of the dynamic interplay between military institutions and political control, socioeconomic change, dynastic finances, and cultural values.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2017 

This special issue of Journal of Chinese History makes the case that military institutions are essential for understanding Chinese history. Our goal is to engage a broad audience instead of talking exclusively to specialists in military history. Thus, rather than an institutional account of, say, the imperial guard, or detailed campaign narratives, readers will find here exploration of the dynamic interplay between military institutions and political control, socioeconomic change, dynastic finances, and cultural values.

What do we mean by military institutions? Whether formal, informal, or, as was most often the case, a shifting mix of the two, “institution” here is used as a shorthand for both the rules of the game and specific state organizations and programs of lasting duration and significant scale. “Military” refers here to affairs pertaining to soldiers and armed forces, usually but not always subject to state authority. Among the military institutions that all four contributors examine in some detail are armies (including their recruitment, training, and maintenance), mobilization mechanisms (including the acquisition, delivery, and consumption of war matériel), and military high command (including its composition, organization, and status).

A central concern of all dynasties, war required the mobilization of economic and social resources, often on a vast and sustained basis. Historians working on other regions and other times have shown that military institutions are closely tied to a wide range of issues, from the state's reach, economic development, and social change to technological innovation, the environment, and definitions of identity. Long ago, the eminent scholar of medieval English history J.O. Prestwich stressed the need to “consider war in its wider aspects, seeking to link it with the forms and methods of government, the social structure, the economy and habits of thought.”Footnote 1 Historians have articulated military institutions’ significance in diverse ways, perhaps the most famous being the Military Revolution (and its ongoing historiographical permutations) and the military-industrial complex (or more recently the military-industrial-academic complex). Such explanations stress that military institutions are important not merely for the relatively small proportion of the total population under arms, but because they are bound directly and indirectly to a far broader swathe of society. Determining, documenting, and satisfying military needs, such as food, supplies, fuel, weapons, manpower, housing, transportation, education, training, and diverse expertise guaranteed that military institutions had a multifaceted impact on many sectors of society. The demands and opportunities of military institutions shaped expectations, experiences, and strategies in life. The chaos and suffering of war might be the first thing that one associates with military institutions, but in most periods most people escaped such dire experiences. During wartime and peacetime, land taxes, compulsory militia service (that might be commuted to additional taxes), interaction with locally garrisoned military personnel (which varied from exploitation and competition to commercial partnership and marriage alliances), opportunity for economic advancement through long- or short-term military service, commercial gain through servicing military personnel's needs, social and economic hardship accompanying the loss of father, husband, or brother, or physical relocation were among the ways military institutions touched people's lives.

For policy makers, military institutions existed to protect the dynasty against its enemies at home and abroad. The ideal was a powerful military force that would defend the realm, project force beyond dynastic borders as needed, suppress internal insurrection, and deter uprisings. Its costs would be low to both the court and the people. Finally, military commanders would obey the throne. As this special issue shows, balancing these three desiderata was an enduring challenge. To begin with the last point, deciding military commanders’ role in the state apparatus was a recurring question answered in different ways. Were military commanders to have a major voice in determining policy or was their primary function to carry out plans formulated by the throne and dynastic administrators? By what criteria were senior commanders selected and evaluated? This special issue shows that such decisions varied according to recent historical memory, the severity of external threats, and issues of ethnic allegiance. Similarly, debates about how to staff, feed, house, train, motivate, and discipline armies often hinged on a rich mix of lessons drawn from historical examples, the exigencies of current socioeconomic conditions, political and personal alliances, and perception of dangers at hand.

MILITARY HISTORY AND CHINESE HISTORY

Scholars have long appreciated war's importance for Chinese culture. The history of military thought, especially during the classical period, has figured prominently in our understanding of Chinese intellectual history.Footnote 2 In recent decades, interest has broadened to cultural dimensions of war, as specialists in literature, art, and the history of emotion have explored the ways men and women expressed their experience of chaos, dislocation, suffering, and the struggle to understand their place in an unpredictable world through poetry, essays, letters, and painting.Footnote 3 Analysis of military narratives’ culturally constructed nature has sharpened our understanding of what sources can and cannot tell us.Footnote 4 Likewise, exploration of martial display's role in political culture has shed light on issues of rulership, ethnicity, and technologies of representation.Footnote 5

Scholars have also shown increasing sensitivity to the ramifications of war's fiscal and logistical demands in China. Although the fullest such studies tend to focus on the eighteenth, nineteenth, and twentieth centuries, decades ago in his Sanctioned Violence in Early China, Mark Lewis famously argued that military demands were a key catalyst in the early Chinese state's development.Footnote 6 Military mobilization required the extraction of resources, including foodstuffs, fodder, livestock, fuel, labor, silver, and a vast array of raw materials. Such extraction, especially for extended campaigns, necessitated administrative efficacy, merchants’ cooperation, and popular acquiescence if not support. Several studies have shown that as the costs of war and military preparation increased in the late nineteenth and especially early twentieth centuries, so rose administrative, economic, and political thresholds needed for success.Footnote 7 War mobilization also depended on specialized expertise, ranging from strategy and tactics, cartography, and logistics to weapons manufacturing, medicine, prognostication, and the occult.Footnote 8 Mobilization's social impact included both resentment (even resistance) of heavier tax burdens and the seizure of livestock and food, on the one hand, and new opportunities for social and economic advancement for mercenaries who fought for competitive wages, merchants who supplied armies on campaign, and officials who battened on the enhanced flow of imperial largesse intended to keep military personnel loyal and motivated, on the other.Footnote 9 Finally, debates about the interplay among war, weaponry, and technological innovation, a well-developed historiographical issue among scholars of Western Europe, have produced innovative works that both analyze developments in China and integrate them into global accounts of the early modern world.Footnote 10

In sum, our special issue takes advantage of an increasingly sophisticated and broad-ranging appreciation of the multifaceted influence of war and military preparations for understanding the Chinese past. Our essays deliberately avoid an exclusive focus on war to consider the underappreciated role of military institutions and their interplay with society, economics, religion, and culture during times of both war and “peace,” peace being a relative term. Given the size of the Tang, Song, Ming, and Qing dynasties’ territory, military action was nearly always underway somewhere. Further, in the case of military institutions, there is no reason to focus solely on either war or peacetime. Arrangements created for wartime mobilization often persist long after fighting ended, albeit often in different forms. To give just one example, the acquisition of high-quality horses in large numbers for use in military conflict, often with steppe foes, was a persistent concern through these centuries, gaining greater urgency in times of war but never fading completely from dynastic concerns. Horse administration nicely illustrates four points: the persistence of military institutions during the peacetime; the close ties among military imperatives, trade policy, and foreign relations; military institutions’ important role in shaping land tenure and the environment; and finally the opportunity to integrate Chinese historical experience into transregional narratives, as institutions to acquire steppe horses by largely sedentary regimes were common to much of eastern Eurasia.Footnote 11

THE ESSAYS

A few words are in order about what this special issue does and doesn't include. The essays here examine the Tang, Song, Ming, and Qing dynasties, roughly the period from 600 to 1800. Some colleagues may object that a span of 1,200 years is too short to capture military institutions’ full historical arc, and certainly no one doubts the critical importance of developments in earlier and later periods of history.Footnote 12 Nonetheless, we suggest that 1,200 years does give a sense of both recurring patterns and distinctive developments (more on this below). Spanning the Tang-Song transformation, the Song-Yuan-Ming transition, and the incorporation of China into world and regional empires (as well as regional and then global economies), the period from 600 to 1800 witnessed enormous changes in the composition of political and cultural elites, the structure and capacity of the state, economic life, and demography, not to mention social and cultural life. We hope that the essays as a group combine a sense of each dynastic period's distinctive features with a thematic coherence across the centuries.

The contributors address overlapping issues, but the ways they frame questions often originate in historiographical concerns particular to their time period. David Graff opens with the question of the whether the military loomed larger in the Tang dynasty than other periods, as the eminent Edwin Pulleyblank once suggested. Peter Lorge structures his essay as a rebuttal to past characterizations of the Song state as militarily weak and Song society as indifferent, even adverse, to the military and military men. David Robinson takes up the cudgels against past descriptions of the Ming state as incapable of change because it was slavishly bound to the dynastic founder's dictates. Finally, Dai Yingcong's essay reflects recent interest in issues of ethnic allegiance and Qing institutional innovations. If period-specific historiographical issues shape each essay, attention to variation across time and space figures prominently in all our accounts, which consider full-scale military mobilization for extended periods of time, lesser campaigns of limited duration, and “peacetime” institutions. Difference according to place, which included the capital, the hinterlands, the borders, and abroad, likewise influenced military institutions and their impact.

Conspicuously absent within our 1,200-year span are essays on the Liao, Jin, and Yuan dynasties. The special issue did in fact originally include a chapter each on the Liao and Yuan dynasties, but as anyone with experience in collaborative projects will attest, scholarly plans seldom survive first contact with life's reality. For various reasons and at various points, two colleagues were forced to withdraw from the project, and production deadlines (not to mention the small pool of specialists in Liao and Yuan military history) regrettably meant that finding replacements was not possible.

Recapitulation of all important features of military institutions during the Liao, Jin, and Yuan dynasties is neither possible nor desirable here, but three points do merit brief mention. First, all three dynasties faced the organizational and logistical questions springing from the integration of steppe warfare, including most especially mounted archers, and infantry forces, questions that had resurfaced for nearly a millennium when the Kitan conquered the Sixteen Prefectures, a northern slice of what had been the Tang dynasty early in the tenth century. Second, the Liao, Jin, and Yuan confronted variations of another enduring challenge, that is, how to best exploit military resources of a subjugated population that was exponentially larger, wealthier, and more technologically advanced than the conqueror. Finally, and inseparable from the first two points, was the complex question of ethnic allegiance and identity. Below, let us briefly note how those three issues unfolded under the Mongols.

The Mongols’ imperial enterprise is justly famous for the intensity and breadth of the cultural, technological, medical, fiscal, and ethnic interaction it created across much of Eurasia. The Mongols’ willingness to adopt new military technology and organization meant that they fielded armies that integrated men, arms, and organization in ways that almost always gave them a military advantage in the field.Footnote 13 Less explored are the ways the Mongols’ military institutions interacted with social, economic, political, and ethnic developments of the Yuan period. Consider the integration of military personnel and family members of different linguistic and cultural backgrounds. Previous dynasties of Chinese, Tibetan, and Turco-Mongolian origins had incorporated large numbers of soldiers (and of their family members) from within and beyond the Chinese ecumene into imperial forces, operating with various degrees of autonomy and cooperation with regulars. Under the Mongols, however, the sheer scale and diversity of people whose lives were structured around military units forced organizational innovation and produced unintended and lasting consequences at the local and national level. Both the Ming and Qing dynasties drew on facets of Mongol institutional architecture, most especially garrisons composed of families with hereditary military responsibilities.Footnote 14

Viewed in its entirety, our 1,200-year span reveals several striking things. First is the state's consistently large annual expenditure devoted to military expenses, most especially to soldiers’ wages. Graff suggests that in the late eighth century, almost two-thirds of central and provincial government revenue went to support military costs. Lorge, Robinson, and Dai offer a strikingly similar estimate; the Song, Ming, and Qing governments all dedicated approximately 70 percent of their budget to military expenditures. Wartime expenses often sent military costs soaring even higher, which prompted surtaxes, calls for donations, and other ad hoc measures. None suggest that the figures mentioned above are anything more than preliminary approximations. The fiscal dimensions of military expenditures at the dynastic, provincial, and county levels promise a fruitful line of future research that will reveal much about state administrative capacity, intragovernmental operations, and strategies for securing the cooperation of non-state actors, most especially merchants, who played an essential role in acquiring and delivering grain from the early Song period onward.

Another suggestive set of numbers is army size. Our authors provide the following estimates: 600,000 Tang soldiers in the mid-eighth century to as many as one million in the early ninth century; somewhere between 600,000 and 900,000 in the Song;Footnote 15 1.2 million for the late fourteenth century and 2 million for the early seventeenth century; and finally 800,000 in the mid-eighteenth century.Footnote 16 Again, these aggregate estimates require clarification and further research. Were they, for instance, full-time professionals, part-time militiamen, mercenaries, or something else? Were they under the command of the imperial government, warlords, or local officials? Some numbers are clearly historiographical artifacts, frequently repeated but seldom scrutinized estimates that date back to early twentieth-century historians working with a small pool of problematic sources or even earlier to contemporary observations unaccompanied by corroborating evidence. Finally, as Graff notes, although the number of men under arms might have been prodigious, it still constituted a small percentage of the population. He calculates the ratio of soldiers to the overall population (or the “military participation ratio,” M.P.R.) for the Tang as ranging between 1:117 and 1:70. If we use the figure of 800,000 soldiers for the eighteenth century, the ratio would be significantly lower for the Qing period, given its markedly larger population (as much as 300 million by 1800, yielding a back-of-the-envelope figure of 1:375)—a stark contrast with the last years of Louis XIV (1:50) and Prussia in 1740 (1:27).Footnote 17

Despite the problematic estimates of military expenditure and army size and the need for proper contextualization, the numbers are still large and remind us that military institutions consumed the vast majority of state resources and that military personnel were by a long measure the dynasty's most numerous employees. Thus, it is not surprising that military institutions drew much attention not just from officials and educated men but from the many people whose lives were shaped directly and indirectly by military imperatives and the institutions designed to satisfy them. As Graff, Robinson, and Dai note, the organization of military forces influenced local governance, social dynamics, and urban geography. Depending on recruitment, garrisoning, and pay practices, military personnel might be closely integrated into local communities, living and working side-by-side with civilian neighbors or they might form socially and culturally autonomous enclaves with limited contact with civilians. Additionally, a strong ethnic dimension during the Yuan and Qing periods shaped settlement patterns for military personnel. Examples include the Yuan court's deployment of guards (wei 衛) dominated by Mongol, and more especially Western and Central Asian (semu 色目), soldiers to strategic sites between Daidu and the south, and Qing segregation policies that prohibited people not registered in banner units from residing in large sections of major urban centers.Footnote 18 Thus, although suggestive, the army's total size only poorly captures military personnel's true significance. Their patterns of interaction with civilian populations, government officials, and religious centers all deserve further attention.

Finally, moving beyond questions of governmental structure, Graff, Lorge, and Dai argue that martial values and practices, seen in literature, theater, and other leisure activities, deeply influenced all levels of society, including highly educated men. The same held true for the Ming period too. Why martial ethos and practices held such an appeal deserves closer attention. In the field of Ming history, it is often asserted that military crises of the late sixteenth and early seventeenth centuries led to a valorization of martiality (shangwu 尚武), but that claim is seldom examined in comparative terms, even within the Ming period, much less the wider sweep of history. The four essays suggest that amidst the great social, economic, and political changes that transformed China between 600 and 1800, martial ethos and practices retained an enduring (but not unchanging) appeal for a variety of people. Lorge in fact goes so far as to argue that martial culture exercised a deeper, wider influence in Song society than did Confucian values and lifeways, which were largely limited to highly educated men and their immediate families. We might hypothesize that martial ethos's appeal resulted from the higher political and social status of military commanders, officers, and common soldiers of the day than surviving sources suggest or that it was tied to other factors such as the formation of ethnic and gender identities.Footnote 19 In any case, the valorization of martiality was certainly multivalent, and future research will deepen our understanding of its origins, expressions, and reception.Footnote 20

The addition of gender, technology, the environment, popular culture, and ethnicity to our analytical repertoire has significantly revised our understanding of Chinese history. We suggest that appreciation of military institutions’ interplay with economics, society, culture, law, governance, technology, and identity will similarly challenge past assumptions and open exciting new research avenues.

References

1 The comment appears in the published version of “The Problem of Interpretation,” one of his six Ford Lectures presented at Oxford University in 1983.  See Prestwich, J.O., The Place of War in English History, 1066–1214 (Woodbridge: The Boydell Press, 2004), 3 Google Scholar.

2 For a small sampling, see Lewis, Mark, Sanctioned Violence in Early China (Albany: State University of New York Press, 1990)Google Scholar; Pines, Yuri, “A ‘Total War’? Rethinking Military Ideology in the Book of Lord Shang,” Journal of Chinese Military History 5.2 (2016), 97134 Google Scholar; Yates, Robin, “New Light on Ancient Chinese Military Texts: Notes on Their Nature and Evolution, and the Development of Military Specialization in Warring States China,” T'oung Pao Second Series, 74.4/5 (1988), 211–48CrossRefGoogle Scholar.

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5 Waley-Cohen, Joanna, The Culture of War in China: Empire and the Military under the Qing Dynasty (London and New York: I.B. Tauris, 2006)Google Scholar; Chang, Michael, A Court on Horseback: Imperial Touring and the Construction of Qing Rule, 1680–1785 (Cambridge: Harvard University Asia Center, 2007)Google Scholar; Robinson, David, Martial Spectacles of the Ming Court (Cambridge: Harvard University Asia Center, 2013)Google Scholar.

6 Hans van de Ven, “Public Finance and the Rise of Warlordism,” Modern Asian Studies 30.4 (1996), 829–68.

7 Waldron, Arthur, From War to Nationalism: China's Turning Point, 1924–1925 (Cambridge; New York: Cambridge University Press, 1995)Google Scholar; Chongyi, Feng and Goodman, David, eds., North China at War: The Social Ecology of Revolution, 1937–1945 (Lanham: Rowman & Littlefield Publishers, 2000)Google Scholar.

8 Perdue, Peter, “Military Mobilization in Seventeenth and Eighteenth-Century China, Russia, and Mongolia,” Modern Asian Studies 30.4 (1996), 757–93CrossRefGoogle Scholar; Yates, Robin, “The History of Military Divination in China,” East Asian Science, Technology, and Medicine 24 (2005), 1543 Google Scholar; Sawyer, Ralph, “Martial Prognostication,” in Military Culture in Imperial China, edited by di Cosmo, Nicola (Cambridge: Harvard University Press, 2009), 4564 Google Scholar; Butler, M.A., “Hidden Time, Hidden Space: Crossing Borders with Occult Ritual in the Song Military,” in Battlefronts Real and Imagined: War, Border, and Identity in the Chinese Middle Period, edited by Wyatt, Don J. (New York: Palgrave Macmillan, 2008), 111–49CrossRefGoogle Scholar.

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10 Andrade, Tonio, The Gunpowder Age: China, Military Innovation and the Rise of the West in World History (Princeton: Princeton University Press, 2016)Google Scholar. For fuller bibliographic citations, see Robinson's essay in this special issue.

11 Beckwith, Christopher, “The Impact of the Horse and Silk Trade on the Economies of T'ang China and the Uighur Empire,” Journal of the Economic and Social History of the Orient, 34.3 (1991), 183–98Google Scholar; Skaff, Jonathan, “Horse Trading and other Material Bargains,” in idem, Sui-Tang China and Its Turko-Mongol Neighbors: Culture, Power, and Connections, 580–800 (Oxford: Oxford University Press, 2012), 241–71CrossRefGoogle Scholar; Mitsutaka, Tani 谷光隆, “A Study on Horse Administration in the Ming Period,” Acta Asiatica 21 (1971), 7398 Google Scholar; Gommans, Jos, “Warhorses and Post-Nomadic Empire in Asia, 1000–1800,” Journal of Global History 2 (2002), 121 CrossRefGoogle Scholar.

12 For an excellent point of departure, see Graff, David, Medieval Chinese Warfare 300–900 (LondonRoutledge, 2002)CrossRefGoogle Scholar.

13 Allsen, Thomas, “The Circulation of Military Technology in the Mongolian Empire,” in Warfare In Inner Asian History, edited by Di Cosmo, Nicola (Leiden: Brill, 2002), 265–92Google Scholar; May, Timothy, The Mongol Art of War: Chinggis Khan and the Mongol Military System (Yardley: Westholme, 2007)Google Scholar; The Mongol Conquests in World History (London: Reaktion Books, 2012)Google Scholar.

14 Ch'i-ch'ing, Hsiao 蕭啟慶 (Xiao Qiqing), The Military Establishment of the Yuan Dynasty (Cambridge: Council on East Asian Studies, distributed by Harvard University Press, 1978), 34 Google Scholar.

15 Wang Zengyu 王曾瑜 suggests that the size of the Song army (including both the imperial and provincial forces) grew quickly in its early decades, from approximately 380,000 in the first reign to 660,000 by 997, reaching more than one million men by 1000 and then decreasing to roughly 910,000 by 1020.  See Tseng-yü, Wang (translated by David Wright), “A History of the Sung Military,” in The Cambridge History of China, Volume 5: Sung China, 960–1279 AD, Part 2, edited by Chaffee, John W. and Twitchett, Denis (Cambridge: Cambridge University Press, 2015), 220 Google Scholar.

16 The figure of 800,000 for the Qing period includes only full-time soldiers.  Information on army size for the Yuan period is incomplete and scattered.  Gaohua, Chen 陳高華 (“Lun Yuandai de junhu” 論元代的軍戶, Yuanshi luncong 元史論叢 1 [1982], 75)Google Scholar suggests that in 1274, one-sixth of the total population of North China was registered in military households, with a higher percentage in strategically critical areas.  To the steppe components of the Yuan army, which included Mongols (in the broadest sense) and Turks, were added Kitan, Jurchen, and Chinese personnel in several stages, including an estimated 300,000 soldiers registered as “newly submitted troops” 新附軍, that is, former Southern Song troops.  See Hsiao, The Military Establishment, 12–17.  Lesser numbers of Koreans, Ossetians, and others also were incorporated.  Some state categories, such as “newly submitted troops,” retained lasting significance, influencing wages and organization well into the 1350s.  See Xiaoxin, Wang 王曉欣, “Yuandai xinfujun wenti zaitan” 元代新附軍問題再探, Nankai xuebao 南開學報 (zhexue shehui kexueban 哲學社會科學版) 2 (2009), 118–22Google Scholar.

17 The figures for M.P.R. in France and Prussia come from Graff's essay. The population estimate for the Qing is based on Myers, Ramon and Wang, Yeh-Chien, “Economic Developments, 1644–1800,” in The Cambridge History of China, Volume 9, The Ch'ing Empire to 1800, Part One, edited by Peterson, Willard (Cambridge: Cambridge University Press, 2002)Google Scholar, Table 10.1, 568.

18 Hsiao, The Military Establishment, 45–46; Yuandai de suwei zhidu” 元代的宿衛制度, Guoli zhengzhi daxue bianzheng yanjiusuo nianbao 國立政治大學邊政研究所年報 3 (1975)Google Scholar, rpt. in idem, Nei beiguo er wai Zhongguo: Meng Yuanshi yanjiu 內北國而外中國:蒙元史研究 (Beijing: Zhonghua shuju, 2007)Google Scholar, vol. 1, 247–48; Elliott, Mark, The Manchu Way: The Eight Banners and Ethnic Identity in Late Imperial China (Stanford: Stanford University Press, 2001), 88132 Google Scholar; Rhoads, Edward, Manchus & Han: Ethnic Relations and Political Power in Late Qing and Early Republican China, 1861–1928 (Seattle and Washington: University of Washington Press, 2000), 3542 Google Scholar.

19 Davis, Richard (Wind against the Mountain: The Crisis of Politics and Culture in Thirteenth-century China [Cambridge: Council on East Asian Studies, Harvard University, 1996])CrossRefGoogle Scholar argues that Song elite male self-perceptions developed in tandem with their views of women and Jurchen and Mongol warriors to the north.

20 Zinan, Yan (“On the Divergent Implications of Archery: Discussing the Poetry of Nobles and Officials on Manchu and Han-Chinese Cultures,” in Political Strategies of Identity Building in Non-Han Empires in China, edited by Fiaschetti, Francesca and Schneider, Julia [Wiesbaden: Harrassowitz Verlag, 2014], 197224)Google Scholar discusses how poetry related to archery and the bow could be a vehicle to air views on ethnic and cultural identity as well as political vigor.  In different ways, both Don Wyatt and Kathleen Ryor seek to dissolve simple martial-civil dichotomies.  See Wyatt, “Unsung Men of War: Acculturated Embodiments of the Martial Ethos in the Song Dynasty” and Ryor, Wen and Wu in Elite Cultural Practices in the Late Ming,” in Military Culture in Imperial China, edited by di Cosmo, Nicola (Cambridge: Harvard University Press, 2009), 192–218 and 219–42Google Scholar, respectively.