J.M.W. Turner: Sketchbooks, Drawings and Watercolours

ISBN 978-1-84976-386-8

Joseph Mallord William Turner Lecture Diagram 22: Geometry of a Parabola (after John Hamilton) c.1810

Joseph Mallord William Turner 1775–1851
Lecture Diagram 22: Geometry of a Parabola (after John Hamilton) circa 1810
Turner Bequest CXCV 66
Pen and ink, pencil and watercolour on wove paper 681 x 485 mm
Watermarked ‘1794 | J WHATMAN’
Inscribed by Turner in red watercolour ‘22’ top left and ‘Hamilton’ top centre and by Ruskin in red ink ‘66’ top right
Accepted by the nation as part of the Turner Bequest 1856
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

How to cite

Andrea Fredericksen, ‘Lecture Diagram 22: Geometry of a Parabola (after John Hamilton) c.1810 by Joseph Mallord William Turner’, catalogue entry, June 2004, revised by David Blayney Brown, January 2012, in David Blayney Brown (ed.), J.M.W. Turner: Sketchbooks, Drawings and Watercolours, Tate Research Publication, December 2012, https://www.tate.org.uk/art/research-publications/jmw-turner/joseph-mallord-william-turner-lecture-diagram-22-geometry-of-a-parabola-after-john-r1136487, accessed 19 May 2022.