Wren,Hooke and Graphical Practice

Jardine Boris Jardine Nick , “Critical editing of early-modern astronomical diagrams”, q.v.

Birch Thomas , The history of the Royal Society of London (4 vols, London, 1756–57), ii, 12.

Geraghty Anthony , The architectural drawings of Sir Christopher Wren at All Souls College, Oxford: A complete catalogue (Aldershot, 2007), 253 (no. 391).

Bennett Jim , “Cosmography and the meaning of sundials”, forthcoming in Biagioli Mario Riskin Jessica (eds), Nature engaged: Science in practice from the Renaissance to the present (New York, 2011).

For work within the history of science focused on gesture, see Sibum Heinz Otto , “Reworking the mechanical value of heat: Instruments of precision and gestures of accuracy in early Victorian England”, Studies in history and philosophy of science, xxvi (1995), 73–106, and Schaffer Simon , “Experimenters' techniques, dyers' hands, and the electric planetarium”, Isis, lxxxviii (1997), 1997–83. The classic starting point for studies of gesture, both for the history of science and more broadly within the anthropology of technology, remains Marcel Mauss, “Techniques of the body”, Economy and society, ii (1973), 1973–88.

For recent examples of such analyses, see Kusukawa Sachiko MacLean Ian (eds), Transmitting knowledge: Words, images, and instruments in early modern Europe (Oxford, 2006), particularly Remmert Volker R. , “‘Docet parva pictura, quod multae scripturae non dicunt’: Frontispieces, their functions, and their audiences in seventeenth-century mathematical sciences”, 239–70, and Pantin Isabelle , “Kepler's Epitome: New images for an innovative book”, 217–37.

Ruffner James , “The curved and the straight: Cometary theory from Kepler to Hevelius”, Journal for the history of astronomy, ii (1971), 178–94; Bennett J. A. , “Hooke and Wren and the system of the world: Some points towards an historical account”, The British journal for the history of science, viii (1975), 1975–61, particularly pp. 49–60; Steven Shapin, A social history of truth: Civility and science in seventeenth-century England (Chicago, 1994), 266–91. The 1664 comet has been extensively discussed. For a general survey, see Yeomans Donald K. , Comets: A chronological history of observation, science, myth, and folklore (New York, 1991), chap. 4; and, for an entry to more recent work, Meinel Christoph (ed.), Grenzgänger zwischen Himmel und Erde: Kometen in der Frühen Neuzeit (Regensberg, 2009), 78–90, and Boschiero Luciano , “Giovanni Borelli and the comets of 1664–65”, Journal for the history of astronomy, xl (2009), 2009–30.

On this point, see also the editors' introduction to the recent special issue on the biographies of scientific images in Nuncius, xxiv (2009), 279–89, p. 284–5.

Hevelius Johannes , Prodromus cometicus (Gdansk, 1665), 20.

The geometrical problem is presented by Hooke as a direct quotation. Hooke breaks off his English exposition saying “the Problem as I received it, is this” and then provides Wren's text in Latin; Hooke Robert , Lectures and collections (London, 1678), 41. The problem is accompanied by an engraved plate with six diagrams to accommodate the different cases referred to in the text. Wren had proposed the problem to John Wallis and the latter's solution also survives; see Bennett , “Hooke and Wren” (ref. 7), 50, n. 103.

Bennett , “Hooke and Wren” (ref. 7), 52, n. 117 presents the scheme — Or rather Hooke's version of it — As a record of the determination of the comet's path from observations. But the regular presentation in five-day intervals, starting from before observations began, shows that it operates in the opposite direction.

For those not inclined to experiment, an animation of the diagram is available online at http://www.mhs.ox.ac.uk/compassandrule/kiosk/wren (accessed 29 March 2010). Note that as Wren's first diagram is viewed from the south, the third diagram has south at the top and the comet might better be described as rising towards the ecliptic.

For the creation of multiple view drawings, see Lefèvre Wolfgang , “The emergence of combined orthographic projections”, in Lefèvre Wolfgang (ed.), Picturing machines, 1400–1700 (Cambridge, MA, 2004), 209–44, and for competing Renaissance interpretations of the Vitruvian prescription see also Filippo Camerota's contribution to the same volume, “Renaissance descriptive geometry: The codification of drawing methods”, 175–208, particularly pp. 196–7. For the interconnections of Wren's mathematical, anatomical and architectural drawings, see Gerbino Anthony Johnston Stephen , Compass and rule: Architecture as mathematical practice in England, 1500–1750 (New Haven, 2009), where Wren's comet drawing is discussed at pp. 87–90.

Fale Thomas , Horologiographia (London, 1593), f. 5v.

How Wren constructed his parallel lines is not entirely clear. Euclid provides a purely geometrical but laborious operation, which reappears in innumerable texts on practical geometry. Parallel rules (special-purpose mathematical instruments for just this task) are known from the sixteenth century, with the publication of Fabrizio Mordente's design in 1584; see Camerota Filippo , Il compasso di Fabrizio Mordente: Per la storia del compasso di proporzione (Florence, 2000), 158. However, according to Maya Hambly, the instrument does not seem to have been common until the eighteenth century; see her Drawing instruments, 1580–1980 (London, 1988), 111–13. In any case, most early examples are also too small for the transfers required in a drawing the size of Wren's. Tee-squares were also not widely known and the variety of directions of Wren's lines would have rendered this technique awkward or impossible. Perhaps the most likely practical solution was to slide a square against a rule, both of them core instruments of geometrical drawing practice.

For recent discussions of the term ‘theoric’, which extend it beyond the traditional astronomical realm, see Bennett Jim , “Knowing and doing in the sixteenth century: What were instruments for?”, The British journal for the history of science, xxxvi (2003), 129–50; Johnston Stephen , “Theory, theoric, practice: Mathematics and magnetism in Elizabethan England”, Journal de la Renaissance, ii (2004), 2004–62; and Dupré Sven , “Visualization in Renaissance optics: The function of geometrical diagrams and pictures in the transmission of practical knowledge”, in Kusukawa MacLean (eds), op. cit. (ref. 6), 1–39, particularly pp. 26–33.

Ward Seth , Vindiciae academiarum (Oxford, 1654), 30.

Wren does not seem to have been entirely persuaded by his own straight line hypothesis, and the comet's possible deviation from rectilinear motion was important in Hooke's framing of the issue of planetary motion; see Bennett , “Hooke and Wren” (ref. 7), 52–5, 57–8.

Note that Wren already had experience of the difficulties of accommodating observation and theory. He commented that it would be a hopeless task to devise a model for the form of Saturn that would account for all the published observations; see Bennett J. A. , “Christopher Wren: Astronomy, architecture, and the mathematical sciences”, Journal for the history of astronomy, vi (1975), 149–84, p. 157. Wren clearly had an explicit sense that observations are not simply given but have to be considered and weighed, with those deemed less adequate or accurate rejected.

Booker P. J. , A history of engineering drawing (London, 1963), and Deforge Yves , Le graphisme technique: Son histoire et son enseignement (Seyssel, 1981). For important and more nuanced recent work on both machines and architecture, see Lefèvre (ed.), op. cit. (ref. 13).

See, for example, the phenomenological approach of Rosand David , Drawing acts: Studies in graphic expression and representation (Cambridge, 2002).

Bermingham Ann , Learning to draw: Studies in the cultural history of a polite and useful art (New Haven, 2000). Bermingham's important study focuses on the emergence of drawing as an amateur artistic pursuit and, though occasionally referring to cartography and mathematics, considers science principally in relation to landscape and life studies.

Ingold Compare Tim , “Beyond art and technology: The anthropology of skill”, in Schiffer Michael Brian (ed.), Anthropological perspectives on technology (Albuquerque, 2001), 17–31, and his Lines: A brief history (London, 2007), chap. 6. Drawing can be explored through reconstruction, using historical drawing instruments and materials to follow past prescriptions. For an example, see the video of architectural drawing at http://www.mhs.ox.ac.uk/compassandrule/kiosk/drawing (accessed 29 March 2010), though for practical reasons this introduces some anachronisms by using eighteenth-century instruments to illustrate Renaissance drawing practice.