On the Mathematics of the Perspective of the Arnolfini Portrait and Similar Works of Jan van Eyck Author(s): John L. Ward Source: The Art Bulletin, Vol. 65, No. 4 (Dec., 1983), pp. 680-686 Published by: College Art Association Stable URL: http://www.jstor.org/stable/3050378 . Accessed: 25/01/2011 19:26Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=caa. . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact firstname.lastname@example.org.
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THE ART BULLETIN DECEMBER 1983 VOLUME LXV NUMBER 4
savagery, and the "golden" style of Claude to depict the coming of civilization? In short, here, as in many other well-documented instances, Bingham seems to have tried to utilize the principles of high art, as he had learned them from art manuals and other sources, to immortalize the development of the Western frontier. Museum of Art, Carnegie Institute Pittsburgh, PA 15213
DiscussionOn the Mathematics of the Perspectiveof theArnolfini Portrait and Similar Works of Jan van
EyckJohn L. WardThe arguments and evidence presented by David L. Carleton in his note, "A Mathematical Analysis of the Perspective of the Arnolfini Portrait and Other Similar Interior Scenes by Jan van Eyck," in the March, 1982, issue are inadequate to support any of what I take to be his major claims. These are as follows: (1) Van Eyck's paintings, the Annunciation of the Ghent Altarpiece, the Dresden Triptych, the Ince Hall Madonna, the Rolin Madonna, the Arnolfini Portrait,1the Madonna of Canon van der Paele, and the Lucca Madonna, employ a perspective with "two vanishing areas centered at the two foci of an ellipse,"2 which is therefore referred to by Carleton as elliptical perspective. (2) The Arnolfini Portrait has the basic optical effects of a convex mirror, which were derived from one such as that on the rear wall of the painting.3 (3) "Jan's convex mirror was also present at the time of the execution of his other interior scenes" and its use "led to his
development of a consistent application of a mathematical theory of perspective, best called elliptical perspective."4 To substantiate his first point, Carleton presents perspective drawings of the seven Van Eyck paintings discussed. Five of these drawings reverse the layout of the paintings without explanation or apparent purpose. On the basis of these drawings, Carleton concludes that each picture has a perspective with two central vanishing areas, that these are both lowered in each subsequent picture, until the last one, the Dresden Triptych, returns to an earlier, less monumental form, and that the two vanishing areas and their sequential lowering "lead to the conclusion that Jan probably did have a mathematical theory of perspective, and that he consistently applied and developed this theory."" Carleton insists on the presence of only two vanishing areas for each of the pictures that he discusses instead of the three mentioned by G. Ten Doesschate or the four mentioned by Panofsky for the Arnolfini Portrait.6 However, the imprecision of Carleton's drawings and the omission of certain orthogonals greatly exaggerate the consistency of the convergence into two vanishing areas. To be sure, the floor and ceiling converge in two precise vanishing areas in the Arnolfini Portrait and in more approximate ones in the Van der Paele Madonna and the Dresden Triptych. But the Rolin Madonna has two vanishing areas for the floor alone, the upper one of which is slightly higher than the vanishing area for the orthogonals of the upper wall; the Ghent Altarpiece Annunciation has only one coherent vanishing area, that of the floor orthogonals,' and the Ince Hall and Lucca Madonnas are quite inconsistent in perspective.8 The Lucca Madonna is perhaps most instructive, since Carleton follows Panofsky in giving it a late date and one might expect it to be one of the clearest examples of a fully developed, mathematically consistent, "elliptical" perspective. My perspective drawing of the Lucca Madonna (Fig. 1) shows that the floor does not converge accurately to a single area (if the receding lines of the rug were projected, the disparity would be much greater), in contrast to the floor of the Arnolfini Portrait and that of the earliest work analyzed, the Ghent Altarpiece Annunciation,
II have retained the familiar title of the painting for convenience, study of its iconography("De matrimonio althoughPeterSchabacker's Reconcontracto:Jan van Eyck's'Arnolfini'Portrait ad morganaticumsidered," Art Quarterly, xxxv, 1972, 375-98) reopens the question of the
identities. subjects' of the the Perspective Arnolfini Portraitand Other SimilarInteriorScenesby Janvan Eyck,"2 David L. Carleton, "A Mathematical Analysisof
observesthat,with arenot citedby Carleton, on Van Eyck'sperspective respect to the two central panels, "von fiinfzehn Linien sich nicht weniger als vierzehngenau in einem Punkte schneiden"("Perspektive bei Jan van Eyck," Repertorium fiir Kunstund Bildarchitektur wissenschaft, xxxv, 1912, 28. For a perspectivedrawing of the outer left panel, see fig. 19 in my article,"Hidden Symbolismin Jan vanEyck's Annunciations," Art Bulletin, LVII,1975, 196-220). By contrast,
Art Bulletin, LXIV, 1982, 119.34 5 6
Ibid., 123-24. Ibid., 124. Ibid., 121.
Ibid., 119. See Panofsky, Early Netherlandish Painting, Cambridge, Mass., 1953, I, 203, and G. Ten Doesschate, Perspective: Fundamentals, Controversials, History, Niewkoop, 1964, 139f. 7 Of course the orthogonals of the beams at the juncture of the side walls
and ceiling in the two outer panels will cross somewhere.However,in sharp contrastto the consistencywith which the floor orthogonalsare of eachbeamcross each otherwell before plotted,the threeorthogonals they meet any of the orthogonalsfrom the opposite beam. A careful is constructed deliberately analysisclearlyshows thatthe floorprojection studies and carefullyas a single system. G.J. Kern,whose fundamental
of the two beams no attemptwhateverwas madeto join the orthogonals in a single vanishingarea.Carleton's drawing,on the other perspective hand, seems to imply that VanEyckorganizedhis spaceby plottingthe convergence,on each side of the picture, of one of the many floor orthogonalswith an orthogonalof one of the beams.Such a procedure but also the strictaccuracy of the floor convergence, not only disregards implies that the artist would be more concerned over pictorial not evident to a viewerthanover those that would be disrelationships was inaccurate. evidentif the convergence of orthogonals turbingly 8 The Ince Hall Madonna,presentlyowned by the NationalGalleryof is now universally Victoria,Melbourne, by scholarsas not by recognizedVan Eyck (see U. Hoff and M. Davies, The National Gallery of Victoria, Melbourne, Les primitifs flamands, I, Corpus de la peinture des anciens Pays-Bas meridionaux au quinzieme sikcle, xII, Brussels, 1971, 29-50). Although I believe it to be a good copy after a lost Van Eyck, any conclu-
made. mustbe cautiously sionswith respectto the perspective
1 Lucca Madonna, perspective drawing which do.9 Figure 1 also shows that the sides of the throne base meet at a point immediately next to the vanishing area of the descending orthogonals of the cloth of honor,1o and that the orthogonals along the walls are entirely independent of these areas of convergence. These deviations from a two-point central perspective construction seriously weaken the claim that a mathematical system of perspective has been used, or any method based on two areas of convergence. Generally speaking, in Van Eyck's pictures the more the accuracy of the convergence of orthogonals can be visually estimated (because of length, uninterrupted visibility, number, proximity, and situation within the same plane), the more care Van Eyck takes to converge his orthogonals accurately. Hence the strict accuracy of the floors of the Arnolfini Portrait, the Ghent Altarpiece Annunciation, and the central section of the Rolin Madonna in contrast to the floors of the Ince Hall and Lucca Madonnas and the side sections of the Rolin Madonna's floor. Hence, too, the lesser accuracy, in the pictures analyzed by Carleton, of the orthogonals to the sides of the picture, which are 9 For a perspectivedrawingand analysis of the Arnolfini Portrait,seeKern (as in note 7), 29-30 and fig. 1, or Die Grundziige der linearperpektivischen Darstellung in der Kunst der Gebriider van Eyck und ihre Schule, Leipzig, 1904, pl. Iv. For the Ghent Altarpiece Annunciation, see note 7. 10In the Van der Paele Madonna, there is also a separate area of convergence for the orthogonals of the throne base, but it is lower than that of the floor. 11I assume that these are the de