Joseph Mallord William Turner

Geometric Diagrams

c.1818–19

View this artwork by appointment, at Tate Britain's Prints and Drawings Rooms

Artist
Joseph Mallord William Turner 1775–1851
Medium
Dimensions
Support: 177 x 256 mm
Collection
Tate
Acquisition
Accepted by the nation as part of the Turner Bequest 1856
Reference
D13819
Turner Bequest CLXX 4 a

Catalogue entry

The circular diagrams on this page probably relate to Turner’s ongoing research and preparation for his lectures as Professor of Perspective at the Royal Academy. Turner first gave his series of six lectures in 1811 and continued to revise them in subsequent years.1 Based on the date that the paper in this sketchbook was manufactured (1815), and the date of other sketches in this book (1818–20), these diagrams are likely to relate to the 1819 lectures.
The various diagrams on this page are all concerned with circles, and are likely to be connected to Turner’s explanation of geometry, rather than linear perspective, which he covered in the first lecture of the series.2 Specifically, the diagram at the top right, which shows a circle intersected by a square, matches one of Turner’s lecture diagrams which Finberg called, ‘Circle with figure: Trigonometry’ (Tate D17007; Turner Bequest CXCV 37), and the large diagram at the bottom left may be related to diagrams of ‘Spherical Trigonometry’ (Tate D17009; Turner Bequest CXCV 39).3 Both were made on paper with watermarks of 1817, so may have been made around the same time. These may therefore be studies for Turner’s perspective diagrams.
The watercolour blotches in several shades of red, the yellow spots and the blue and orange marks at the right of the page near the binding are not related to the diagrams but are likely to have occurred when Turner was painting other pages in the sketchbook (D13818–D13828; CLXX 4–13).

Thomas Ardill
August 2009

1
Maurice Davies, ‘Perspective Lectures at the Royal Academy’, Evelyn Joll, Martin Butlin and Luke Herrmann (eds.), The Oxford Companion to J.M.W. Turner, Oxford 2001, p.223.
2
Ibid.
3
Finberg 1909, I, p.583, CXCV 37, 39.

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