Joseph Mallord William Turner

Lecture Diagram 22: Geometry of a Parabola (after John Hamilton)


In Tate Britain

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Joseph Mallord William Turner 1775–1851
Pen and ink and graphite on paper
Support: 681 × 485 mm
Accepted by the nation as part of the Turner Bequest 1856
Turner Bequest CXCV 66

Catalogue entry

This is one of two diagrams numbered 22, made by Turner to illustrate Lecture 2 as Professor of Perspective at the Royal Academy; see also D17035; Turner Bequest CXCV 65. They relate to his discussion of conic sections and reference to the elder Thomas Malton’s explanation of the rare circumstances in which the parabola and hyperbola can arise.1 With a third diagram, numbered 23 (D17037; Turner Bequest CXCV 67) they show the geometry of the parabola and are based on illustrations from John Hamilton, Stereography; or a Complete Body of Perspective in all its Branches (1738, fig.84, no.1). This diagram is based on fig.73 from Hamilton. According to Maurice Davies, the diagrams have ‘little relevance to the discussion and Turner may have chosen to include them merely because Malton mentions works on conic sections by [Hamilton] at this point’.2 See Turner’s Perspective Sketchbook (Tate D07384–6/TB CVIII folios 17 verso–18 verso) for preliminary sketches and notes.
Thomas Malton [Senior], A Compleat Treatise on Perspective ...(1775); Turner, ‘Royal Academy Lectures’, circa 1807–38, Department of Western Manuscripts, British Library, London, ADD MS 46151 L folio 9 verso. For earlier versions of related material, see D folio 5 verso and E folios 18 verso–19.
Davies 1994, p.165.
Technical notes:
Peter Bower states that the sheet is Super Royal size Whatman paper made by William Balston and Finch and Thomas Robert Hollingworth, at Turkey Mill, Maidstone, Kent. He writes that all ‘the sheets in this batch have some streaking across the sheet, probably from a fault in the sizing’.1
Notes in Tate catalogue files.
Blank, save for an inscription by an unknown hand in pencil ‘68’ top left.

Andrea Fredericksen
June 2004

Supported by The Samuel H. Kress Foundation

Revised by David Blayney Brown
January 2012

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