Notes:
1. P Steadman, Vermeer's Camera: Uncovering the Truth Behind the Masterpieces, Oxford University Press 2001
2. ibid Chapter 5 pp.73-100
3. ibid Chapter 6 pp.101-117
4. ibid.p.106. In the book I point out that this finding does not actually depend on knowing the position of the back wall from the reflection in 'The Music Lesson', and could have been discovered without that information.
5. Walter Liedtke of the Metropolitan Museum in New York made this suggestion in a Colloquium preceding the opening of an exhibition, 'Vermeer and the Delft School' at the National Gallery, London, 16th June 2001
6. Paul Taylor, personal communication. Taylor and Gowers's reasoning runs essentially as follows. Suppose p is the probability of one of Vermeer' s ten canvases being the same height - within reasonable bounds of accuracy - as its projected image. What is the probability of this occurring randomly in six cases out of ten? The answer is p to the sixth power multiplied by '10 choose 6': If p is assumed to equal 1 in 10, the odds are therefore roughly 1 in 5000. If p is 1 in 5, the odds are more like 1 in 300. Walter Liedtke in a review of Vermeer's Camera in The Burlington Magazine (October 2001 pp.642-3 n.4) offers the suggestion that this geometrical phenomenon might somehow be the result of Vermeer using canvases of standard dimensions, pointing to Figure 65 (p.130) in the book which illustrates the comparative sizes of all the painter's pictures of interiors, to scale. Even if the sizes had been standardised, that would not have accounted for the geometrical result. However as my Figure 65 makes clear, Vermeer's canvases - with the exception of the two pairs of similar-size pendants - differ widely in their dimensions. The six canvases under consideration here are particularly varied in size (Figure 51 p.104).
7. Walter Liedtke, ibid; JØrgen Wadum, 'De tent van Vermeer', Vrij Nederland, 28th Apri12001, p.68
8. Wadum, ibid, claims that the versions of these two diagrams which appear in the book are wrongly drawn and do not match the text. Perhaps, he says, the draftsman did not follow the author's instructions. In fact I drew them myself, and they are perfectly correct. The passage in question says that, in a camera of the type shown here in Figure 2, "the image is upside-down and reversed left-to-right." This is perhaps a little ambiguous, and so may be the cause of Wadum's confusion. I had intended the reader to understand that the two symmetry operations are carried out in sequence: first the rotation through 180°, then the reflection about a vertical axis. Comparable diagrams, showing the orientation of the image in several types of camera obscura, are given in J H Hammond, The Camera Obscura: A Chronicle, Adam Hilger, Bristol 1981 p.4
9. See Liedtke op cit p.643
10. Steadman op cit p.26 n.6
11. ibid pp.107-9 and Figure 53 p.108. Judith Haskins and Leo Stevenson (personal communications) have both suggested that Vermeer's booth might also perhaps be reflected in the cylindrical body of the brass pitcher in 'Young Woman with a Water Jug'. Certainly there is a greyish-black rectangular stripe at the centre of this reflection. This painting is not one for which I have so far made a three-dimensional reconstruction of the space depicted, since no part of the floor is visible by which to determine the position of the viewpoint. However it is not out of the question that such a reconstruction might now be made, given that we have exact dimensions for the casement and the lions' head chairs, as well as the map of the Seventeen Provinces, and thus might find the viewpoint by trial and error. It would then be feasible to test whether the reflection in the jug corresponds to a cubicle of the right size and at the right distance. Another mirror reflection of the back of the room which might repay further analysis is that in the central spherical body of the brass chandelier in 'Allegory of Paintng'.
12. David Bomford in discussion at the Colloquium mentioned in n.5 above
13. Steadman op cit p.100
14. J M Montias, Vermeer and His Milieu: A Web of Social History, Princeton University Press, Princeton NJ 1989 p.176 n.20 and Figure 31
15. Wadum op cit
16. Steadman op cit p.113
17. Wadum op cit. Wadum thinks that the fact that, in this arrangement for the camera, the image is mirror-reversed, means that the paintings should therefore also show the room in mirror image, i.e. with the windows at the right rather than the left. His objection thus overlooks all the discussion in the book of how the reversed image in this type of camera can, relatively simply, be rectified.
18. J Elkins, personal communication
19. Wadum, op cit, says that 17th century Dutch artists never painted with the light coming from the right-hand side - so overlooking Vermeer's own 'Guitar Player' and 'View of Delft', not to mention any number of Pieter de Hoochs and other contemporaries.
20. Steadman op cit pp.116-7. Among the few exceptions are the map in the left foreground of 'The Love Letter', but this is in deep shadow, painted very schematically, indeed hardly recognisable as a map at all; and the painted lids of the matching virginals in the two pictures in the National Gallery in London. As I argue in the book, I believe these two virginals to be one and the same instrument, with different anamorphic landscapes substituted by Vermeer for any possible decoration on the real lid. Both the decoration on the virginal, and the painting on the far wall at upper left, in 'Lady Standing at the Virginals' are based, it transpires, on a composition by Pieter Groenewegen - a friend of Vermeer's father - 'Mountain Landscape with Travelers' (1640), differently cropped in each case. (See W Liedtke, ed, Vermeer and the Delft School, catalogue of an exhibition held at the Metropolitan Museum of Art, New York and the National Gallery, London, March-September 2001; Yale University Press, New Haven and London 2001, p.403 and Figure 293.) This picture has an elongated horizontal format (38 x 68 cm), although not quite so elongated as the version on Vermeer's virginal lid, as it would appear when viewed frontally (see Steadman, op cit pp.116-7). Perhaps Vermeer was able to carry out the process of 'anamorphing' Groenewegen's landscape by means of the camera obscura.
21. See W Liedtke op cit p.643; Wadum op cit; and W Liedtke, talk given at Art and Optics' conference, New York Institute for the Humanities, 1st/2nd December 2001, published at www.artandoptics.com; consulted January 2002.
22. M Kubovy, The Psychology of Perspective and Renaissance Art, Cambridge University Press, Cambridge p.122
23. Steadman op cit p.80, p.83, Figure 36 p.82, and Figure 37 p.83. This almost obsessional quality to Vermeer's perspective technique leads him arguably into some odd decisions. In 'Woman with a Pearl Necklace' for example there are two peculiar unexplained patches of light in the otherwise deeply-shaded area in the foreground, beneath the table. These must surely be glimpses of a white floor tile beyond one of the table legs. Since no other parts of the floor are visible, it is impossible to say whether the tile occurs in the 'right' place. But my guess is that it does, and that Vermeer put it in for no other reason than that he could see it.
24. ibid p.47
25. J A Welu, 'Vermeer: his cartographic sources', Art Bulletin 57, 1975 pp.529-47
26. It is the second edition of Adriaan Metius, lnstitutiones Astronomicae & Geographicae, Willem Jansz. Blaeu, Amsterdam 1621, open at the first two pages of Book III, 'On the Investigation or Observation of the Stars' . See J Welu, 'Vermeer's Astronomer: observations on an open book', Art Bulletin 68, 1986 pp.263- 7
27. See Steadman op cit, Appendix B (pp.171-6) in which dimensions for the maps, pieces of furniture and musical instruments, calculated from the perspective reconstructions, are compared with the known sizes of these various items.
28. ibid pp.96- 7 and notes to Table B3 pp.174-5
29. R Hawkins, personal communication. Hawkins is an architect, artist and photographer. He makes the suggestion that Vermeer has brought about the reduction in the projected sizes of the images of the casements through having to make large adjustments to the focusing of his camera. Ian Gillies (personal communication) points out that the two window sills in 'The Glass of Wine' do not line up precisely - as they do for example in 'The Music Lesson' - again suggesting that the images of the two windows have here been 'collaged' together.
30. Wadum op cit
31.Liedtke op cit p.643 n.6, citing C Willemijn Fock, 'Werkelijkheid of schijn. Het beeld van het Hollandse interieur in de zeventiende-eeuwse genreschilderkunst', Oud Holland 112, 1998 pp.187-246; also the talk cited in note 21 above
32. P Thornton, Seventeenth-Century Interior Decoration in England, France and Holland, Yale University Press, New Haven and London 1978 p.86
33. Steadman op cit. p.115 and Figure 55
34. C Shields, review of Vermeer's Camera at www.irisgallery.co.uk, January 2002. Shields even suggests (personal communication) that Vermeer might actually have painted the ceramic tiles themselves with house paint, in black and white, in groups of four, in order to gauge the visual effect.
35. Liedtke op cit p.643 n.6, citing Fock, op cit. On this question of ceiling construction, Fock in fact confines her attention largely to one painting by Emanuel de Witte, in which, she says, the beams 'do not run parallel to the facade as they ought to, but perpendicular to it.' Meanwhile Fock actually illustrates (Figure 1, p.188) a 17th century room in the Centraal Museum in Utrecht which has the beams running towards the window wall.
36. M van Leusen, personal communication reporting on conversations with Willem Weve
37. Willem van der Bas, personal communication
38. Wadum, op cit.
39. On the other hand, if the room was not exactly rectangular in plan, then the pattern of floor tiles would not meet the walls in neat rows of half tiles, as it appears - to do. Sherman DeForest makes this point (personal communication) and emphasises that there are always inaccuracies and adjustments in the setting out of any real tile work, which might possibly be detectable in Vermeer's outlines.
40. A K Wheelock Vermeer and the Art of Painting, Yale University Press, New Haven, Conn. 1995 p.94
41. See Steadman op cit pp.121-2 and Plates 5 and 6
42. ibid p.128. Se also Figure 62, p.126
43. R Hawkins and L Stevenson, personal communications
44. The map is reproduced in modern facsimile in H L Houtzager, G C Klapwijk, H W van Leeuwen, M A Verschuyl and W F Weve (eds) De Kaart Figuratief van Delft, Elmar, Rijswijk 1997. See sheets 45 (p.131), and 46 (p.133), details from which are shown in Steadman op cit Figure , 20 p,60
45. Ian Gillies, personal communication
46. Steadman op cit. p.143, and p. 156-7.
47. G B della Porta, Magia Naturalis, 1st edn. Naples (4vols) 1558; 2nd edn. (20 vols) 1589. This quotation from Natural Magick by John Baptista Porta, a Neapolitane, trans T Young and S Speed, London 1658 p.364
48. For a review of such ideas put forward by a range of writers see Steadman op cit pp.30-37. W Liedtke in the Burlington Magazine review quibbles with my claim that this literature goes back 'more than a hundred years', and says it starts with A Hyatt Mayor in 1946. I said 'a hundred years' because I start my account with Joseph Pennell's article of 1891. Paul Claudel raised the idea of Vermeer using the camera in a lecture given in 1934.
49. D Hockney, Secret Knowledge: Rediscovering the Lost Techniques of the Old Masters, Thames and Hudson, London and Viking Studio, New York, 2001
50. In discussion at the' Art and Optics' conference mentioned in note 21 above; and in debate at the Royal Society, London, 26th October 2001
51. Steadman op cit pp.110-11
52. L Gowing, Vermeer, Faber, London 1952 p.137
53. Wadum op cit
54. K M Groen, I D van der Kerf, K J van den Berg, and J J Boon, 'Scientific examination of Vermeer's Girl with a Pearl Earring' in I Gaskell and M Jonker (eds), Vermeer Studies, National Gallery of Art, Washington and Yale University Press, New Haven, Conn. 1998 pp.168-83. See pp.170-1
55. E M Gifford, 'Painting light: recent observations on Vermeer's technique' in I Gaskell and M Jonker (eds), Vermeer Studies pp.184-99. See p.187
56. J Elkins, text of a lecture given at the' Art and Optics' conference mentioned in note 21 above, and published at www.artandoptics.com . Consulted January 2002.
57. Personal communications with Stead Steadman (no relation), Quentin Williams and others. Williams, on the other hand, saw a water-colourist making a landscape inside a camera obscura in Bristol in the 1960s. The camera tent was improvised from a Windsor chair and a blanket. The painter was working in white body colour - almost gouache. However he was unwilling to enter into conversation.
58. Leo Stevenson, personal communication
59. ibid
60. David Marshall, personal communication
61. For a discussion see Steadman op cit pp.153-4
62. J Wadum, 'Vermeer in perspective' in A K Wheelock, ed, Johannes Vermeer, catalogue of an exhibition held at the National Gallery of Art, Washington and the Mauritshuis, The Hague, November 1995 to June 1996; Yale University Press, New Haven and London 1995, pp.67-69; and J Wadum, 'Vermeer and spatial illusion' in The Scholarly World of Vermeer, Museum van het Boek/ Museum Meermanno-Westreenianum, The Hague; Waanders Publishers, Zwolle 1996, pp.30-49. See p.48
63. Steadman op cit p.154
64. W Liedtke, op cit