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Nian divides this image into six layers (ceng) of overlapping images, each with the same eponymous grid (quadro) that aided the European quadraturisti in transferring their original cartoons to walls.70 The implication of Nian’s grid is that the contents of each image layer corresponded with various squares in the grid and could therefore be recreated simply by scaling the contents of any given square in the grid onto a larger square.

      Each image occupies progressively less space relative to the layer that precedes it. An elaborate architectural frame provides the frontmost layer of the complete, ungridded view, and the five layers behind it show the different groupings of figures, each smaller than the one before, which recede into the background one lateral slice at a time. Each individual layer of the image shows only the figures and objects occupying that single slice of the spatial construction. The figures and objects in a given layer are therefore of a consistent size, respectively either larger or smaller than those that follow or precede them. This multipart illustration suggests that the procedure for creating such a richly detailed image requires both the firm structure of a grid and the spatial awareness to identify the various layers of an image in order to produce a view that successfully appears to recede into the distance. However, Nian’s accompanying commentary is frustratingly incomplete: “These picture-layers are piled up in the spatial recession method [yuanjin zhi fa, literally ‘method of nearness and distance’]. The above five pictures are clear and will not be discussed further. When painting people in spatial recession, you can take the sizes of the six layers as your models.” These techniques were far from common knowledge, and Nian challenges his readers by assuming that they could fully understand the visual instructions without his explaining either the picture or the unusual procedure required to reproduce it.

      On the next page of illustrations, which continues the explanation of this process and its outcome, Nian uses an oblique view of this layer system to expand on how to depict figures in a receding perspectival space (figure 2.13). The five example images all depict the same scene: three children, each holding toys such as a fish on the top of a stick or a pointed lotus dangling from another stick, are sketched out under a canopied ceiling, similar to the content on the previous page. The individual images are again gridded, but also now numbered along both the horizontal and vertical axes. Each increasingly smaller image has progressively larger margins to indicate the growing area overlapped by the image above it according to Nian’s layering method. The brief text accompanying this page explains how to create this type of image by placing sequentially smaller figures in each layer as on the previous page, and concludes with Nian’s comment that “if you use this method to paint, your paintings will possess the same marvelous deep recession as in nature.” Although Nian does not explain exactly what “this method” is, careful examination of the images reveals it: regardless of the size of the individual images relative to the complete composition, the figures and objects always occupy the same number of

      2.11 “Layer method” for spatial recession. From Nian Xiyao, The Study of Vision. The Bodleian Libraries, University of Oxford, Douce Chin. B. 2, p. 54v.

      squares in the grid, suggesting a consistent representational ratio that can be adapted as necessary to a surface of any size.

      Scholars have repeatedly misread these two illustrations (figures 2.11 and 2.13) as instructions for stage backdrops or Chinese opera stages,71 likely because the object that Nian actually represents is a miniature European perspective theater.72 The Augsburg printmaker Martin Engelbrecht (1684–1756) and his workshop exclusively produced this popular and sophisticated eighteenth-century tabletop amusement between the 1720s and 1770s. Such theaters included five to eight small scenery-like sheets placed in parallel slots inside a box and viewed as framed by an architecturalized open façade at the front of the box, all the pieces cooperating to suggest a scene with deep recession. Engelbrecht perspective theaters were not the type of thing that the Jesuits brought into China, but rather the sort of singular curiosities that enterprising officials in Guangdong acquired directly from foreign traders and sent to the court in order to curry favor with the recipient, whether a court official or the emperor himself. Engelbrecht did not begin producing his theaters until after Nian’s time in Guangdong

      2.12 Detail of the full completed image produced by the “layer method.” From Nian Xiyao, The Study of Vision. The Bodleian Libraries, University of Oxford, Douce Chin. B. 2, p. 54v.

      had ended, suggesting that one of these theaters appeared either in Beijing or at Huai’an sometime in between 1725 and The Study of Vision in 1735. It would certainly have been an appealing example of visual and pictorial illusionism as well as a useful tool for teaching how to demonstrate the depth cues that support illusionistic painting. However, nothing in either Nian’s commentary or the images themselves suggests that he understood what this object was, or that it was structurally related to a European theater and theater scenery. During this period in China, purpose-built theaters were only just beginning to be constructed, and dramatic performances did not employ large-scale painted scenery as in Europe.73 Furthermore, what Nian represented as the center of each overlapping layer is precisely the area of each perspective theater image sheet that is not illustrated. In the various layers of prints used in the miniature theaters, the central area was often left open to allow the viewer to see clearly through the various overlapping layers into the distance, which was depicted only on the card containing the vanishing point, inserted in the last slot in the box. In misreading the perspective theater as part of his investigation of spatial recession,74 Nian not only

      2.13 Detail of the second illustration of the “layer method” for spatial recession. From Nian Xiyao, The Study of Vision. The Bodleian Libraries, University of Oxford, Douce Chin. B. 2, p. 55r.

      created a compelling document of a European object not otherwise known to have circulated in eighteenth-century China, but also presented a unique method for producing illusionistic paintings.

      Nian’s treatise culminates in the ninth section (57r–75r) with an extended visual lesson on cast shadows created with rays of light from a single light source, represented as diagonal solid lines extending over a figure to the ground. The cast shadows are merely silhouetted with dotted lines tracing the blank shape of the shadow on the ground below the object; not with dark infilled or cross-hatched patches that would otherwise give the shadow substance. This section begins with simple generic rectilinear and curved polyhedrons to establish the method, but the final case study objects are specifically Chinese forms, including a hexagonal basin stand, ceramics such as the teapot (figure 2.8), a man in fur-lined aristocratic Manchu winter dress and hat (figure 2.14), and a stalking tiger next to an arched door (figure 2.15). The man and the animal immediately make a cultural

      statement in favor of the ruling Qing, recalling two leaves from Yongzheng’s well-known album of twelve costume portraits. One album leaf depicts the emperor in Mongol winter costume similar to Nian’s figure (figure 2.16), although without the slit robe skirt and with the conspicuously Mongol addition of a gold hoop earring. The stalking tiger is depicted half-hidden in the leaf that depicts Yongzheng in Western dress (figure 2.17), one of two portraits in this costume that further illustrate his interest in Western things. Tigers were common prey for the Manchus and Mongols in the hunting grounds north of the Great Wall, eagerly sought in a non-Han

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