Joseph Mallord William Turner

Lecture Diagram 19: Conic and Cylindrical Sections (after Thomas Malton Senior)


In Tate Britain

Prints and Drawings Room

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Joseph Mallord William Turner 1775–1851
Watercolour on paper
Support: 674 × 999 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CXCV 62

Catalogue entry

In a section on curvilinear perspective in Lecture 2, given as Professor of Perspective at the Royal Academy, Turner addresses the role of conic sections.1 Like most of his material for this lecture, the section is based on A Compleat Treatise on Perspective in Theory and Practice on the True Principles of Dr Brook Taylor (1775) by the elder Thomas Malton (1726–1801), while Diagram 19 is loosely founded on three diagrams from the book (pl.VII, figs.27–9). According to Maurice Davies:
the central part illustrates the situation when a circle is positioned on the axis of the eye. The rays joining the eye to the circle make a cone with the circle forming the base and the eye at the apex. Three different possible picture positions are shown as planes intersecting the cone. As the perspective representation of the circle is always a plane intersection of a cone, it must, by definition, be a conic section; that is, either a circle, ellipse, parabola or hyperbola. The right-hand part and [Diagram 20; Tate D17033; Turner Bequest CXCV 63] show some of the arrangements that can arise when the circle is not on the axis of the eye.2
However, as Davies adds, ‘the left-hand part showing planes intersecting a cylinder does not occur anywhere in Malton (and in fact has no relevance to what Turner writes about at this point)’.33
Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 BL MS L folio 9 and verso. For earlier versions of related lecture material, see D folio 5 and E folio 10 verso.
Davies 1994, pp.163–4.
Ibid., p.320 note 48.
Technical notes:
Peter Bower states that the sheet is Double Elephant size Whatman paper made by William Balston, at Springfield Mill, Maidstone, Kent. The largest group within the perspective drawings, this batch of paper shows a ‘grid-like series of shadows that can be seen within the sheet in transmitted light. This appears to have been caused by a trial method of supporting the woven wire mould cover on the mould’. Because this is the only batch he has seen with such a feature, Bower believes that ‘it may have been tried on one pair of moulds and for some reason never tried again’. He also writes that it is ‘not the best Whatman paper by any means; the weight of this group is also very variable and the moulds have not been kept clean during use’.1
Notes in Tate catalogue files.

Andrea Fredericksen
June 2004

Revised by David Blayney Brown
January 2012

Read full Catalogue entry

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