Counting Vermeer


1. The Scientific Examination of Works of Art: Its Potentials and Its Limitations

Arthur K. Wheelock, Jr.

Counting Vermeer features a new type of scientific examination of paintings: computer-generated ‘weave maps’. These weave maps provide information about threads and weave patterns with such precision that scholars can compare the character of the canvas supports of different paintings. This knowledge can help determine, for example, whether canvas supports were made from the same bolt of cloth. As a consequence, weave maps are an extremely useful tool for assessing questions of dating, pendant relationships, and even authenticity. This volume, the result of collaborative efforts by conservators, art historians, scientists, and computer specialists, and produced through the initiative of C. Richard Johnson, Jr., demonstrates the ways in which the study of weave maps has helped inform our understanding of a number of paintings by Johannes Vermeer.

The volume opens with the excellent chapter on X-radiography by Petria Noble and Ige Verslype. After providing a historical overview of the use of X-radiography in the study of paintings, which began in earnest around 1925 with the work of Alan Burroughs at the Fogg Art Museum at Harvard University, Noble and Verslype narrow their focus to its use in Vermeer scholarship. They demonstrate how this examination technique reveals compositional changes and the buildup of paint layers as well as losses and other damages that have occurred over time. As Noble and Verslype note, X-radiographs also provide information about the canvas because they register the various densities of the lead-bearing ground layers covering that support.

The history of how these canvas supports have been analyzed over the last sixty years is the subject of the following chapter. Michiel Franken examines the origins and character of canvas supports, while noting that studying them is often difficult because most of these supports are no longer visible due to (re)linings. As a result, they can generally only be studied indirectly through X-radiography. X-radiographs, however, do not actually record the density of the fabric itself, but its imprint on the radio-absorbent lead white in the ground layers. Partly for this reason, with the exception of Rembrandt van Rijn, no systematic study of the canvas supports used by Dutch painters has ever been undertaken.1

Assessing weave patterns from information provided by X-radiographs has heretofore been done by hand count, which is a tiresome and inexact process. With the advent of digital X-radiographs, however, computer-generated weave maps can now be created. These provide much more information about the warp and weft of canvas supports than previously possible. As William Sethares explains in his chapter, software enabling this scientific examination technique (described in Chapter 4) can be applied to the user’s own digital X-radiographs. Sethares recommends that this software, which is downloadable from this volume’s website, be used in conjunction with manual thread counts to validate and verify its results, the reason being that its calculations are numerically based and differ in character from manual thread counts.

Cover image
Johannes Vermeer
Girl with a Pearl Earring, c. 1665-1667
The Hague, Koninklijk Kabinet van Schilderijen Mauritshuis, inv./ 670

In Chapter 5 Sethares expands upon this information to explain the software’s mathematical underpinnings (the Fourier technique). The weave maps created by this software may be displayed as either thread maps or angle maps. The first of these maps displays variations in thread density across the canvas, and the second shows deviations in the angle of the threads from their true horizontal and vertical orientations. The author stresses that reading these maps requires an awareness of the computational science underlying them if one is to avoid reaching faulty conclusions. Sethares provides examples of weave and angle maps from a few of Vermeer’s paintings to demonstrate their appearance and explain how they should be interpreted.

The culminating chapter in this volume, Rick Johnson’s essay on ‘Exploiting Weave Maps’, discusses some of the practical consequences of this technological research on Vermeer studies. Although a few earlier scholars have dealt with thread counts in Vermeer’s paintings, and have made careful charts of the master’s canvas supports, the information available through computer-generated weave maps advances our knowledge about them.2 As Johnson notes, thread maps, or ‘density maps’ have been helpful in issues of authentication of Vermeer paintings, in particular Young Woman Seated at a Virginal (L36). The attribution of this painting, which was often doubted in the past, was proven to be correct when it was determined that its canvas support came from the same bolt as that of The Lacemaker (L29).3 Similarly, this examination process revealed that The Geographer (L27) and The Astronomer (L28) were painted on identical canvas supports, important information in the ongoing discussions as to whether Vermeer created these paintings as pendants.4 To date, Johnson and his team have identified six weave match pairs among Vermeer’s paintings.

Angle maps of canvas supports provide information about weave distortions, or cusping patterns, which are important for determining whether a painting has been cut or has been preserved in its original format. Johnson notes that most of Vermeer’s paintings have cusping on all four sides. The question then remains: if cusping is absent along one or more of its sides, does one then conclude that the painting has been trimmed? This chapter does not exhaustively evaluate all of Vermeer’s canvas supports, but provides guidelines for future researchers when examining the X-radiographs of his paintings.

This introduction to Counting Vermeer aims to situate the development of computer-generated weave maps into the broader spectrum of Vermeer scholarship. The level of scientific certainty these weave maps provide in determining the character of canvas supports is a welcome complement to previous studies made of oak panel supports for Dutch paintings. Those investigations, including dendrochronological examinations that were first undertaken in the 1970s, have provided much information about the place of origin and the dating of these panels.5 As with all technical studies of paintings, however, the information gained from weave maps must be carefully combined with a host of other art historical and technical approaches when evaluating their significance for interpreting works by Vermeer and his colleagues.

Such an inclusive approach would seem to be self-evident, yet, over the course of the last century, technical studies have not always been fully integrated into art-historical assessments of works of art. Occasionally the failure has come from scientists focused, in a linear way, on the results of a specific line of inquiry without exploring its implications within the broader context of art historical inquiry. Art historians/connoisseurs, on the other hand, have also rejected information gained from scientific investigations if it contradicted their aesthetic assessments of a work of art.

This latter attitude is best demonstrated in a pamphlet published in 1926 by the Dutch art historian Hofstede de Groot: Echt of Onecht? Oog of Chemie? (True or False? Eye or Chemistry?). In his essay Hofstede de Groot pitted connoisseurship against chemical analysis after its results proved that a painting he had attributed to Frans Hals was a forgery.6 Other Dutch art historians in the first decades of the twentieth century were also reluctant to welcome scientific investigations into their studies (see below in regard to two Vermeer fakes made by the same forgers), but it should be said that this field of inquiry was then only in its infancy. Fortunately, a few ground-breaking conservators and scientists soon began to provide a framework for scientific analyses of paintings, none more consequential than Alan Burroughs, with his studies of X-radiographs, or A.M. de Wild, who published his dissertation on the scientific examination of paintings in 1928.7

Because of this volume’s focus on technical and scientific matters, it seems important to reflect for a moment upon how they can inform our understanding of Vermeer’s paintings and their distinctive aesthetic qualities. Virtually all commentaries on Vermeer’s paintings celebrate the powerful yet inexplicable ways in which his works affect the viewer. His works resonate in a realm that cannot be rationally explained, and, indeed, his paintings have often inspired poets. One art lover expressed the life-altering impact of Vermeer’s paintings in the following terms: ‘I, too, was first attracted to Vermeer's work because of his perfect composition and the harmony of his colors. But as I grew older and matured, I began to sense that his work could help me understand my life experience.’8

The intangibles of Vermeer’s distinctive style, coupled with a dearth of documentary evidence about his artistic aspirations, have induced painters, art historians, conservators and scientists to examine his paintings carefully for clues as to how he achieved his effects. Some of the most observant assessments of Vermeer’s painting techniques were penned by artists, among them Philip Leslie Hale, who published a monograph on Vermeer in 1913.9 In his extensive chapter on Vermeer’s techniques, Hale assessed the way Vermeer built up his paintings by laying in his compositions with flat layers of light and shade. He wondered if Vermeer might have painted on a canvas prepared with blue or green because of the tonalities of some of his paintings. He also speculated that Vermeer used yellow lake that had faded away or been removed by overly harsh cleaning.10

In anticipation of later studies about Vermeer and the camera obscura, Hale was fascinated by the distinctive optical qualities of Vermeer’s works, including pointillé touches, modulated edges of forms, soft areas of focus, and the way he eliminated extraneous pictorial elements. Hale particularly admired Vermeer’s ability to arrive ‘at tone by an exquisitely just relation of colour values’, an idea, he continued, that ‘lies at the root of all really good modern painting.’ For him, a prime example of this modernity was Girl with a Pearl Earring (L22):

'There is no other head that one thinks of that is rendered more purely and simply by just light and shade than is this. No painter ever made anything more by simple light and shade than are the eye, the nose, and the mouth of this head… Simply the mouth is made light where it came light, dark where it was dark. And there is no handling visible – one cannot in any way see how the colour was floated on. The form is simply there, perfectly rendered – the means of its making quite concealed'.11

Hale’s fascination with Vermeer’s manner of painting was not unique, particularly in the early 1920s and 1930s, when the artist’s fame was rapidly rising and his paintings were becoming ever more valuable. A number of art historians from those decades, among them Wilhelm Valentiner, followed Hale in characterizing Vermeer’s distinctive style. Ironically, however, some of the most careful assessments of Vermeer’s painting style and techniques in the early twentieth century were made by forgers. The attempts by forgers to create pictorial equivalents to Vermeer’s paintings, and the subsequent efforts of art historians and scientists to uncover the forgers’ methods, had an enormous impact on our understanding of the materials that the Delft master used in creating his distinctive paintings.

The most important of early twentieth-century Vermeer forgers were Theo van Wijngaarden and his friend and collaborator, Han van Meegeren (the same forgers who faked the Frans Hals painting mentioned earlier). Their initial Vermeer forgeries from the mid-1920s,The Lacemaker and The Smiling Girl, both in the collection of the National Gallery of Art, completely fooled connoisseurs who were captivated by the stylistic and thematic connections of these paintings to Vermeer’s known works.12 Indeed, contemporary descriptions sound remarkably like those found in Hale’s earlier monograph. Interestingly, when The Lacemaker and The Smiling Girl first appeared on the market, no Vermeer scholars requested that technical examinations be made of them, even Valentiner, who, when writing about them, observed: ‘To hear almost every year of a newly discovered Vermeer may cause suspicion’.13 One can only assume that Valentiner, like Hofstede de Groot, trusted his eye over chemical analysis.

Although questions about the authenticity of these forgeries had begun to surface in the 1930s, The Lacemaker and The Smiling Girl were donated to the National Gallery of Art in 1937 as authentic Vermeer paintings. Technical examinations subsequently initiated by the Gallery in the 1960s and 1970s finally unmasked them as forgeries. These examinations revealed that each painting had been painted over a partially scraped-down old painting so that the craquelure would appear old. In each instance, the medium was a mixture of oil and a proteinaceous emulsion that would not be affected by organic solvents that were customarily used to test a painting’s age. Nevertheless, while the forger, probably Theo van Wijngaarden in conjunction with Han van Meegeren, had carefully studied Vermeer’s style, he used pigments not available in the seventeenth century. Among the other examinations undertaken in the 1960s was a study of the lead-isotope ratios of the lead white, which revealed that the lead white had been smelted at a different time and place than the lead white in Vermeer’s paintings.14

In conjunction with these investigations into these forgeries, the National Gallery of Art enlisted Hermann Kühn to make a systematic study of Vermeer’s pigments and binding media, the results of which were published in 1968.15 Remarkably, this seminal study, which involved taking samples from thirty Vermeer paintings, involved no interpretation of the results of Kühn’s scientific investigation. Because this information was not integrated into broader questions of Vermeer’s use of materials and how they impacted his style, a huge opportunity was missed to further our understanding of the artist’s work.

The initiative of the National Gallery of Art to pursue technical investigations of its dubious Vermeer paintings to determine if they were forgeries was undoubtedly stimulated by the dramatic court case that had unfolded in the Netherlands between 1945 and 1947 when scientists proved that The Men at Emmaus (Museum Boijmans Van Beuningen, Rotterdam) was a forgery painted by Van Meegeren. The forger’s working techniques and materials were extensively examined by a team of scientists, led by Paul Coremans, Director of the Central Laboratory of Belgian Museums.16 In 1949 Coremans described in detail Van Meegeren’s working procedure, including his use of bakelite as a drying agent. He also carefully analyzed the canvas support that Van Meegeren had used, noting that he had scraped down an old painting and had trimmed the canvas on one side.17 It is historically fascinating that, much as in the circumstances surrounding the Frans Hals forgery in 1924, Coremans made his thorough investigations about a forgery at the behest of a court order.18

Forgers, and those who sought to uncover their techniques and methodology, were not the only ones who probed the mysteries of Vermeer’s work during the course of the twentieth century. P.T.A. Swillens, for example, was convinced that Vermeer carefully and accurately depicted the world around him.19 In his monograph of 1950, Swillens used perspective constructions from Vermeer’s paintings in an attempt to calculate the exact shape and size of the artist’s studio. The fascination with the optical effects found in Vermeer’s paintings led other scholars to explore the possibility that Vermeer used a camera obscura as part of his painting process.20 Such questions led to careful examinations of Vermeer’s painting techniques to assess how he achieved the soft, diffused highlights that were characteristic of his style.21 Technical information gained from careful studies of X-radiographs eventually revealed that Vermeer used a pin to mark the vanishing point of his perspective systems in many, if not most, of his paintings.22

Virtually no one today questions whether scientific examinations of works of art are important for our scholarly assessments, nevertheless, as we try to understand the essence of Vermeer’s paintings, we still find ourselves torn between the seeming polarities of connoisseurship and technical investigation. While these two approaches are different in character – one assessing an artist’s style and the emotional reaction it engenders, and the other utilizing science to understand the materials and their applications in creating a work of art – in the best of circumstances, a symbiotic relationship exists between them. In such instances, technical and scientific examinations help enrich a viewer’s emotional response because they deepen one’s appreciation of, and engagement with, a work of art rather than detracting from it.

Many types of technologies are available to enhance one’s engagement with a work of art, none more important than those that help one have a greater appreciation of what one sees on the surface of the painting. Peering through a microscope is often exhilarating because it allows the viewer to see incredible details that might otherwise be missed with the naked eye. Microscopic examination also can reveal overlapping brushstrokes and glazes that help explain how an artist achieved certain textural and color effects in his painting. Studying a work with ultra-violet light reveals much about the character of the varnish covering its surface. Discovering that a painting has layers of discolored varnish, or has been selectively cleaned in the past, often explains why certain works lack vibrancy, or why their palettes seem muted. Examining a painting with infra-red can provide information about old restorations or repainting, which could explain compositional discrepancies that would otherwise be confusing and lead to faulty conclusions.

Technologies, such as X-radiographs, that penetrate beneath a painting’s surface can often provide a wide range of information that further informs one’s response to a work of art. Neutron autoradiography23 and infra-red reflectography are two different technologies that provide fascinating information about artist’s changes or pentimenti.24 Pigment analyses, whether the result of microscopic examination of paint samples or undertaken with x-ray fluorescence spectroscopy, provide much information about the types of paints artists used, and changes in color that may have occurred over time. The overarching goal of such examinations is to learn more about Vermeer’s artistic process, not only the ways he used his canvas and panel supports, but also how he conceived and built up his compositions, and chose his paints and mediums.25 As with the computer-generated weave maps described in this volume, one hopes that through such examinations it will be possible to come to a better appreciation of how Vermeer achieved his remarkable artistic effects.

An example of the need to have computer-derived weave maps integrated into a broad assessment of Vermeer’s painting style is evident in the assessment of the revelation that the canvas support of Vermeer’s Young Woman Seated at a Virginal, circa 1670-1672 (L36) comes from the same bolt as his Lacemaker (L29), circa 1669-1670. The similarities in these canvas supports, first noted by Libby Sheldon and Nicola Costaras in 2006,26 were confirmed in an article published in 2012 by Walter Liedtke, C. Richard Johnson Jr., and Don H. Johnson.27 This information reinforces arguments that the attribution of Young Woman Seated at a Virginal (L36) to Vermeer is correct. However, further stylistic and technical examinations of the painting revealed that the awkward, large yellow shawl covering the upper portion of the woman’s body was a latter addition and not executed by Vermeer.28 X-radiographs have shown that beneath this shawl is a fully realized garment, with an intricately designed sleeve, that leads gracefully from the neck to the woman’s arm. Pigment analysis has also determined that this lower layer of paint was executed with a different mixture of lead-tin yellow paint than that of the shawl, further reinforcing the conclusion that it is a latter addition.29

As Liedtke, Johnson and Johnson rightly note, the fact that the canvas supports of Young Woman Seated at a Virginal (L36) and The Lacemaker (L29) come from the same bolt does not prove that the two paintings were necessarily painted in the same year. At his death in 1675 Vermeer left ‘ten painter’s canvases’ among the supplies in his studio.30 Paintings from the same bolt of canvas, thus, could have a range of dates depending on how quickly the artist worked and used up his materials at hand. For stylistic reasons, it is likely that Young Woman Seated at a Virginal (L36) dates a few years afterThe Lacemaker (L29).31

Similar issues occur when considering other weave matches that have been found in the canvas supports of other Vermeer’s paintings, including Young Woman Standing at a Virginal (L33) and Young Woman Seated at a Virginal (L34); Woman with a Lute (L14) and Woman Writing a Letter, with Her Maid (L31); and The Astronomer (L28) and The Geographer (L27).32 While information about the canvas supports is important for assessing the dates, and possible pendant relationships of these works, it is but one of a number of factors that need to be considered when making such determinations, including style, paint handling, and compositional relationships. Issues surrounding the proposed pendant relationships of The Astronomer (L28) and The Geographer (L27) are particularly complex because these paintings are not identical in size and they are dated respectively 1668 and 1669.33

This volume establishes the framework for an exciting new stage in our ability to assess the remarkable character of Vermeer’s paintings. Computer-generated weave maps have the potential of providing a firmer foundation for our perceptions and assessments of the choices this Delft master made when selecting his canvas supports. For example, combined with assessments of Vermeer’s style and in conjunction with other technical examinations, information gained from weave maps may well reveal that Vermeer chose different canvas supports because they enhanced certain stylistic effects. As additional paintings by Vermeer and his contemporaries are examined and analyzed, the implications of this examination technique will only grow more significant in our art-historical discourses. It is an exciting prospect!


1 Research on the canvas supports of a number of Rembrandt’s large-scale paintings was carried out in the mid-1950s. In the 1980s, Ernst van de Wetering, in conjunction with the Rembrandt Research Project, made a much broader study about the canvas supports in that master’s work. See: E. van de Wetering, ‘The canvas support’, in: J. Bruijn et al., A Corpus of Rembrandt Paintings, 6 vols., Dordrecht/Boston/Lancaster 1982-2014, vol. 2 (1986), pp. 15-43.

2 N. Costaras, ‘A Study of the Materials and Techniques of Johannes Vermeer’, Vermeer Studies. Studies in the History of Art 55 (1998), p. 147, Appendix 1, pp. 165-166.

3 W. Liedtke, C.R. Johnson Jr., and D.H. Johnson, ‘Canvas Matches in Vermeer: A Case Study in the Computer Analysis of Fabric Supports’, Metropolitan Museum Journal 47 (2012), pp. 101-108.

4 C.R. Johnson Jr., and W.A. Sethares, ‘Canvas Weave Match Supports Designation of Vermeer's Geographer and Astronomer as a Pendant Pair’, in: Journal of Historians of Netherlandish Art 9 (2017), issue 1, (DOI: 10.5092/jhna.2017.9.1.17).

5 J. Bauch, D. Eckstein, and M. Meier-Siem, ‘Dating the Wood of Panels by a Dendrochronological Analysis of the Tree-Rings’, Nederlands Kunsthistorisch Jaarboek 23 (1972), pp. 485-496. Although these scientists did not examine Vermeer’s two panels at the National Gallery of Art in this publication (Girl with a Red Hat and Girl with a Flute), Bauch subsequently undertook those examinations in 1977.

6 C. Hofstede de Groot, ‘Some Recently Discovered Works by Frans Hals’, The Burlington Magazine 45 (1924), p. 87. In the dramatic court fight that ensued over the authenticity of the Merry Cavalier, chemical analyses of the pigments proved that the painting could not have been executed in the seventeenth century. It was also determined, moreover, that the picture was painted with a gummous medium soluble in water. For further information on this court case, see: F. Lammertse and J. van Es (eds.), Van Meegeren’s Vermeers: The Connoisseur’s Eye and the Forger’s Art, Rotterdam 2011 (vol. 6 of Boijmans Studies), pp. 47-49.

7 A.M. de Wild, Het natuurwetenschappelijk onderzoek van schilderijen (diss.), The Hague 1928 (translated as: The Scientific Examination of Pictures, London 1929).

8 Letter from George Sorrels to Arthur Wheelock, September 15, 1995.

9 P.L. Hale, Jan Vermeer of Delft, Boston 1913.

10 Ibidem, pp. 100-101.

11 Ibidem, pp. 220-221.

12 For these paintings, see: A.K. Wheelock Jr., ‘The Story of Two Vermeer Forgeries’, in: A.I. Davies, W.W. Robinson, and C.P. Schneider (ed.), Shop Talk: Studies in Honor of Seymour Slive. Presented on his seventy-fifth birthday, Cambridge (MA) 1995, pp. 271-275 and J. Lopez, The Man Who Made Vermeers: Unvarnishing the Legend of Master Forger Han van Meegeren, Orlando 2008, particularly pp. 52-72.

13 W.R. Valentiner, ‘A newly discovered Vermeer’, Art in America 16 (1928), pp. 101-102.

14 B. Keisch, and R.C. Callahan, ‘Lead Isotope Ratios in Artists’ Lead White: A Progress Report’, Archeometry 18 (1976), pp. 181-193.

15 H. Kühn, ‘A Study of the Pigments and the Grounds Used by Jan Vermeer’, Report and Studies in the History of Art 2 (1968), p. 195.

16 P.B. Coremans, Van Meegeren’s Faked Vermeers and De Hoochs: A Scientific Examination, London 1949.

17 Coremans’ investigations established a model by which technical and stylistic assessments of paintings could be brought together to come to a fuller understanding of the complex character of a work of art, a development that began to bear fruit in the following decades.

18 See: Coremans 1949 (note 16), pp. VII-VIII.

19 P.T.A. Swillens, Johannes Vermeer, Painter of Delft, 1632-1675, Utrecht 1950.

20 C. Seymour Jr., ‘Dark Chamber and Light-Filled Room: Vermeer and the Camera Obscura’, Art Bulletin 46 (1964), no. 3, pp. 323-331. 

21 A.K. Wheelock Jr., ‘Zur Technik zweier Bilder, die Vermeer zugeschrieben sind’, Maltechnik-Restauro 84 (1978), pp. 242-257 and A.K. Wheelock Jr., Vermeer and the Art of Painting, New Haven 1995.

22 See: J. Wadum, ‘Vermeer in Perspective’, in: A.K. Wheelock Jr. (ed.), Johannes Vermeer, Washington, D.C. (National Gallery of Art)/The Hague (Mauritshuis) 1995, pp. 67-74. Wadum identified thirteen paintings with pinholes at the vanishing point. Since then, the number of paintings where pinholes have been discovered has increased to about 20.

23 M.W. Ainsworth et al., Art and Autoradiography: Insights into the Genesis of Paintings by Rembrandt, Van Dyck, and Vermeer, New York 1982.

24 For an assessment of pentimenti in Vermeer’s paintings discovered through infrared reflectography, see: A.K. Wheelock Jr., Vermeer and the Art of Painting, New Haven 1995.

25 A number of excellent articles on Vermeer’s materials and painting techniques appeared in Vermeer Studies (note 2). These include essays by K. Levy-Van Halm, ‘Where did Vermeer Buy His Painting Materials? Theory and Practice’, pp. 137-144; N. Costaras, ‘A Study of the Materials and Techniques of Johannes Vermeer’, pp. 145-168; K.M. Groen et al., ‘Scientific Examination of Vermeer’s Girl with a Pearl Earring’, pp. 169-184; E.M. Gifford, ‘Painting Light: Recent Observations on Vermeer’s Technique’, pp. 185-200; and J. Wadum, ‘Contours of Vermeer’, pp. 201-223.

26 L. Sheldon and N. Costaras, ‘Johannes Vermeer’s “Young Woman Seated at a Virginal”’, The Burlington Magazine 148 (2006), pp. 89-97.

27 Liedtke/Johnson Jr./Johnson (note 3).

28 For a discussion of this shawl and an image of the X-radiograph, see: W.A. Liedtke and A.K. Wheelock Jr., ‘Young Woman Seated at a Virginal’, in: A.K. Wheelock Jr. (ed.), The Leiden Collection Catalogue, (date consulted: September 27, 2017).

29 A similar situation occurs with Woman with a Flute (L25) in the National Gallery of Art, Washington, D.C., which also seems to have been reworked after Vermeer’s death. See: A.K. Wheelock Jr., Dutch Paintings of the Seventeenth Century: The Collections of the National Gallery of Art, Systematic Catalogue, New York/Oxford 1995, pp. 387-393, ill.

30 J.M. Montias, Vermeer and His Milieu: A Web of Social History, Princeton 1989, p. 341, under doc. 364.

31 For an assessment of the stylistic associations of Young Woman Seated at a Virginal with Vermeer’s genre paintings of the 1670s, see: Liedtke/Wheelock Jr. 2017 (note 28).

32 For a discussion of The Geographer and The Astronomer, see: Johnson Jr./Sethares 2017 (note 4).

33 For an argument that these paintings were commissioned separately and in successive years by the Rotterdam collector Adriaen Paedts I, see: W. Franits, Vermeer, London 2015, pp. 228-229. 

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