J O H N P H I B B S

P R O J E C T I V E G E O M E T RY

This paper shows how reliant Brownian design is on projective geometry, not just for the creation of ‘picturable’ views, but for the underlying structure of the landscape. Given initially as a lecture at the Ashridge Summer School, Hertfordshire, on 24 August 2004, the paper is designed to show that mathematics and mathematical tolerance can be brought within the reach of designers and garden historians.

P R O J E C T I V E G E O M E T RY

If the aim of the English landscape movement was to produce something distinct from anything French and sensu stricto original,1 then the most obvious starting point might have been to take out the geometry that characterized the golden age of French gardening – and this is conventionally accepted as what happened: the garden as linear architecture, illustrated in the bird’s-eye views beloved of Leonard Knyff and Johannes Kip and of Charles Bridgeman, was replaced by the garden as nature, typifi ed by the landscape drawing, taken from ground level and advanced by William Kent as an instrument of landscape design.2 Hence, as convention has it, the constant association between painting and gardening peddled by eighteenth-century theorists.3 Indeed painting had become very fashionable, replacing music as ‘the sole object of fashionable care’, even to the point that ‘some of the young nobility are themselves early instructed in handling the pencil’.4 This is what Phillip Southcote meant when he told the Revd Joseph Spence c.1752 that at Stowe, Buckinghamshire, Richard Temple, 1st Viscount and Lord Cobham, had begun ‘in the Bridgeman taste’, and had then moved on: ‘’tis the Elysian Fields that is the painting part of his gardens’,5 and this was the ‘sort of gardening … which Kent and nature have brought us acquainted with; where the supreme art of the Designer consists in disposing his ground and objects in an entire landskip’.6

The wealth of evidence for this conventional account is impressive, but there is another equally constant theme in the eighteenth-century establishment of the English style and that is a sense of some intangible coherence that must inhere in the most wild and naturalistic design. This can be traced well into the seventeenth century with a struggle between the ancient idea that ‘all is number’, that all natural beauty can be, and can only be, interpreted mathematically,7 and Blaise Pascal’s discovery of the beauty in symmetry. Design was either to be based on the use of regular intervals and mensuration, or on a sense that for something to be beautiful it was enough that the viewer should not be inclined to rearrange any part of it (Pascal’s rationale for the effect of symmetry).

19 Wolvercote Green, Oxford OX2 8BD, UK

2 GARDEN HISTORY 34 : 1

It would not be too far-fetched to see a precursor for Pascal in Horace’s paradoxical ‘concordia discors’ and for the dispute in Heraclitus’ and Parmenides’ argument over the changing, or unchanging, universe. Perhaps indeed one should see the tension between order and disorder as inherent in the human perception of the world.

At any rate, both these alternatives had their adherents in English philosophy. On the one hand, Bishop Thomas Burnet argued that before the fall Nature had been organized in a patently mathematical way, and that since then it had been in continuous decay – an argument that might make it the duty of the gardener or place-maker to put nature right again, and by making its mathematical structure apparent, inevitably to restore it to beauty.8

On the other hand, John Locke had established an alternative philosophical position for accepting Nature as it is as a complete work, and this thesis was set out explicitly by the botanist John Ray in 1691.9

Less rigorously logical minds still distinguished between the two ideas of beauty, and asked the question that arises from them: can there be an underlying harmony in the ‘natural error’ of unimproved countryside?

At the beginning of the seventeenth century, Sir Henry Wotton had already distinguished ‘regularity’ from ‘wild regularity’,10 and a generation later the latter class was renamed the ‘Chinese’ by Sir William Temple, who distinguished ‘walks of trees in straight lines, and over against one another’ from a ‘Chinese’ style, generally critical of regularity (i.e. walks of trees), and pursuing a beauty that ‘shall be great and strike the Eye, but without any Orders or Disposition of Parts, that shall be commonly or easily observ’d’.11

This alternative derivation of beauty found its way in the eighteenth-century world of Alexander Pope and Joseph Addison,12 and seems to have been well-established among tourists at that time. So John, Viscount Perceval, claimed to fi nd something similar in Bridgeman’s Stowe, in 1724 ‘Nothing is more irregular in the whole, nothing more regular in the parts, which totally differ one from the other’.13 Sir Thomas Robinson, Bt, had noticed that despite the variety of his art, Kent’s Chinese garden design at Carlton House in Pall Mall, St James’s, still had Nature’s overall unity,14 and the distinction was maintained by Robert Castell, who from what he had read of Chinese gardening described it as ‘an artful Confusion … where, tho’ the Parts are disposed with the greatest Art, the Irregularity is still preserved’,15 and then clarifi ed by Richard Hurd: ‘the careless observer, tho’ he be taken with the symmetry of the whole, discovers no art in the combination’.16

A generation later, Thomas Hale criticized Chinese gardening for having gone ‘beyond the Laws of Nature’ and falling ‘too much into this absolute Wildness’, but his proposed remedy would have been regarded by many as itself Chinese:

It is an Air of Irregularity we advise, not Irregularity itself; there requires more Art by far in this Distribution, than in any other; and there requires afterwards the great additional labour of concealing it. … Every Thing we see should be chosen for its Place, thou it seem the Result of Accident; there should be Order in every Place, though under the Aspect of wild freedom, and a certain Harmony where there is the Aspect of Confusion.17

Now it would be possible to argue from this evidence that the triumph of nature in English gardening was a long, slow one and that each of four or fi ve generations pushed the same argument further than the last in the rejection of mathematical design, and hence made different assumptions about what was ‘irregular’ and what was ‘regular’,

3PROJECTIVE GEOMETRY

but two arguments in particular point to another conclusion. First, if Wotton, or any of the other theorists, had simply sought irregularity in order to imitate nature, they might have achieved it in a single stroke. First, Nature, after all, has never been very diffi cult to imitate, nor, as Horace regretted, does she take long to undo all the tidying of the fork and take charge of arrangements herself. Second, because one cannot really partly drop mathematics: it is only up to a point true to say that 2 + 2 = 5 is less mathematical than 2 + 2 = 4, and that 2 + 2 = 6 is less mathematical again – one equation follows the rules of arithmetic, and the other two do not. Similarly, something is either random or it is not; a randomly created design cannot be ordered, no matter how much it may appear to be – in short, if the components of a design are ‘disposed with the greatest Art’, they cannot also be disposed randomly. From this observation one might infer that even ‘Chinese’ design had some underlying logic or art, and ask what this art was and how it worked.

P R O J E C T I V E V E R S U S M E T R I C A L G E O M E T RY

Following on from this, this paper proposes that one should read the development of the English landscape movement as the steady advance of one way of seeing against another, of China against France, and that this can be expressed mathematically as the advance of angle-based or ‘projective’ geometry against regular or ‘metrical’. The connection with geometry has eighteenth-century precedents: ‘regularity’ at least was used fairly consistently for metrical geometry; but the alternative, projective geometry, was represented by a number of names – to ‘irregularity’, the ‘Chinese’ style and ‘design’, one should add Francis Hutcheson the Elder’s ‘uniformity’.18 These sound like very different things, but in practice I doubt they were.19

The distinction between the two kinds of geometry is sometimes expressed in landscape theory today as the distinction between the ‘ratio’ and the ‘genius loci’, but it was current in the eighteenth century as well. It may be divined in William Mason, who was hostile to the ‘Rule’ (i.e. the ruler or line), which ‘Mechanism … pursues, admires, adores’, but a modernist avant la lettre praised the cube and cone (which are essentially proportions defi ned by their angles).20

Projective is the kind of geometry that is generated by perspective (hence the kind that one might expect to fi nd in a Claudean landscape); it is generated from angles and takes advantage of harmony and balance,21 and is capable of constructions whose underlying harmony is only apparent at specifi c points within the landscape – it is a geometry of illusion, of effect, rather than that of pure form. It can be created on the drawing board with a protractor and compasses, and in the fi eld, whether surveying or setting out, with a theodolite, or by trigonometry.22

Metrical geometry, on the other hand, above all else denotes mensuration and produces regularity and congruity. Mensuration requires the building up of a design from small units (often a yard, or a 10-inch interval). This is the basis of Vitruvian architecture, and surveying and setting out of this sort are to be found in every gardener’s manual.23 Moses Cook, for example, who seems to have worked with Claude Desgots,24 and hence was probably the English designer most directly infl uenced by André Le Nôtre,25 and whose ability as a surveyor was celebrated by Stephen Switzer, wrote up his design for Cassiobury, Hertfordshire, in detail. ‘Detail’, however, is the word, for Cook went no further than showing how to fi t certain fi gures, such as the oval Bowling Green,26 into an existing woodland garden. He congratulated himself on his ability to survey accurately, but never mentioned any overall strategy.27

4 GARDEN HISTORY 34 : 1

Such designs, derived from metrical geometry, are much easier to set out if they are essentially rectilinear (because right angles are the easiest angles to set out on the ground), and small (because this kind of surveying is very prone to accumulating errors, where, for example, the base unit of measurement is 1 inch adrift and is replicated two hundred times in an avenue). Easy though it is to design regularly on paper,28 as the design increases in size, it must be simplifi ed to be practicable, and usually large-scale regular design was confi ned to avenues of one kind or another.

On the plus side, most of the setting out requires only two or three lines, usually made of tarred cord and knotted at prescribed intervals.29 Both the right angle and the tendency to small-scale design were picked on by Humphry Repton to characterize the ‘geometric stile’ (i.e. metric geometry) and emphasized the use of ‘the line and square’ to produce ‘in every direction … ranks of trees, in circles and squares, and triangles, and straight lines, and in every form that the ruler or the compasses could describe’.30

On areas up to a couple of acres, the same basic equipment can be used to set out a design by grids, and the drawn design is then reproduced on the ground by scaling up from the paper. This is less accurate, and is still limited in size, but it was used by Spence and recommended by Leonard Meager, John Rutter and Daniel Carter, Thomas Breaks, and Repton inter alia.31

The need for different equipment for setting out different kinds of geometry was particularly pointed up in Robinson’s observation that Kent’s ‘Chinese’ gardening was carried on ‘without level or line’.32 Both these tools were essential for metrical French design. The line for measuring regular intervals and setting out right angles (e.g. by 3-4-5 triangles); the level on the other hand for making ground fl at;33 for making cut-and-fi ll exercises effi cient (by helping with the calculation of volumes of soil) – and hence for preparing excavations for lakes, particularly where these are regular shapes cut into the ground. (It has often been observed that Lancelot ‘Capability’ Brown made lakes by damming rather than by excavating.34)

Nonetheless, if one looks at the evidence available for Kent’s Carlton House garden, it is obvious that, in both plan and elevation, the design was geometric.35 What distinguishes it from a Bridgeman design in William Woollett’s engraved view is its theatricality – each of the elements, arcades, fl ower beds, terms, etc., builds down the main axis towards the neo-Palladian octagonal temple (1735) at the end, and this theatricality, the subordination of effects, is a trick of perspective and of projective geometry. Since Robinson explicitly stated that Kent did not use the level or line, then one may ask what did he use to achieve this effect, and the only other surveying instrument commonly available at the time was the theodolite, which measures angles and is essential for setting out projective drawings. I therefore conclude that Kent – and of course Brown after him – relied on it.

C R O O M E C O U RT, W O R C E S T E R S H I R E

The landscape at Croome Court, Worcestershire, makes a good starting point for Brown. When he started there c.1751, there was already a house, which Brown was greatly to rebuild and extend, and there had already been some efforts at regular landscaping, not just in the yards and gardens around it, but with an avenue and terrace running east–west in front of the house.36

The Brown design clearly has its elements of metrical geometry. So each of the features that dress the view from the north front, and the pleasure ground and shrubberies themselves, describe an arc with the house at its centre – that is, Cow Pasture, Church Hill

5PROJECTIVE GEOMETRY

Figure 1. Metrical geometry at Croome Court, Worcestershire, is demonstrated by the features that circle the house at a distance of more or less 1500 feet. Projective geometry is demonstrated

both by the number of features on the north–south and west–east axes, and by the spread of features on each side of point blank. Drawing: author

6 GARDEN HISTORY 34 : 1

and South Lawn each run the same distance away from the house (Figure 1). This interval is picked up again by the diversion in the road at the London Lodge and by the bend in the lake.37 Here is a metrical geometry, based on the use of regular intervals, and probably laid out with a line. To this kind of design, Brown brought a more relaxed tolerance, beautifully exemplifi ed in the clumps around the belt in Horse Close and North Field. These are shown on contemporary estate plans to be at more or less regular intervals and at more or less regular sizes, and when one goes to the fi eld, it is still possible to see where they were because the ridge and furrow on the ground on which they were planted was fl attened. Hal Moggridge guessed, correctly, that they were dug six lands apart, and that

Figure 2. Croome: projective geometry determined the distribution of features off the north and south fronts of the house. Drawing: author

7PROJECTIVE GEOMETRY

each was six lands across (a land being one ridge and one furrow). This can be described as regular, metrical planting, but with an unexacting tolerance, akin to setting trees out ten paces apart, because, like paces, the lands are not identical in width.38

However, another geometry provided coordinates for the sites of the buildings. This begins with the north–south line at point blank from the house, and the east–west line of the old avenue, which carries across the (pre-Brown) terrace on the south front of the house (Figure 2).

The fi rst of these lines gives one coordinate for Dunstall Castle (1764–71, attributed to Robert Adam), at Earls Croome, Worcestershire, the second seems not only to have given one coordinate for the Panorama tower (by James Wyatt, 1801), the Boathouse (attributed to Brown himself or Adam), the Chinese Bridge (1751, by William Halfpenny), and the Rotunda (1756–65, Brown or Adam), but also to have determined a long section of the park boundary: east of the Rotunda, for this line meets the lane to Defford at a point where the latter was obviously re-routed.

In the view south from the house, the Owl House (1760–67, attributed to Adam) and an unknown structure (henceforth ‘the obelisk’, which it probably was), were set out at more or less equal angles on each side of point blank (the tolerance here is around 3° for each angle, as shall be shown, at Burton Constable, East Yorkshire, the symmetry is still closer).

A second suite of buildings, on the north side of the house, has two pairs of vignettes set symmetrically about a point blank: the church of St James the Apostle (after 1758–63, by Brown, with interiors by Adam) and the classical deities Camillo, Ganymede, a Vestal and Urania (1760s, by John Cheere); and the ice house (by 1762, attributed to Brown) and temple/greenhouse (1760–67, Adam and Brown).

The orientation of the temple/greenhouse (Figure 3) is determined by Dunstall Castle, which it faces directly. Its architecture – scale, depth, height and columniation – are determined by the landscape. A depression in the fl oor, worn by many thousands of footsteps, shows where a bench was placed, and sitting on it one would have seen the house and Rotunda on the left, Dunstall Castle straight ahead, and the Dry Arch (attributed to Brown, altered by Wyatt, 1797–1807), urn and the statue of the Druid (1793, by Eleanor Coade) on the right, each of them separated by one of the columns of the building.

From the other end of the park, the Owl House faces the grotto (1765–67, attributed to Brown, altered in the 1780s and after) and again the proportions of the architecture seem to have been determined by the landscape design. In fact, there is only one structure in the inner parkland (the Island Pavilion, altered by Coade in 1778) the location, orientation and architecture of which does not derive to some degree from projective geometry.

W O T T O N H O U S E, B U C K I N G H A M S H I R E

The design for Wotton shows that Croome was not a one-off. Here Brown found a site that had already been planted with extensive seventeenth- and early eighteenth-century designs.39 With its several generations of geometry, it does not exhibit Croome’s air of a single hand and a single unifying theory. That said, the two places have much in common: the garden front also has a fi ve-toed patte d’oie (with two avenues, one at point blank, the other towards Chilton Hill, complemented by neatly contrived vignettes to Mars, Jupiter and the Vase). As with the north front at Croome, the sight lines of the Brownian

8 GARDEN HISTORY 34 : 1

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design are precisely symmetrical about the west front of the house, the angles between point blank, Chilton Park Farm and Mars being 50°, giving a total spread of 100°, those with Jupiter and the Vase 20°. As at Croome, there is also a strong line at right angles to point blank offset from the house (Figure 4).

To this symmetry, the Tuscans were added,40 a pair of classical temples, both set out symmetrically about point blank (not visible from the house, so not Claudean), but set out from point blank nonetheless, and so regularly placed that were it not for the example of Croome, one might assume that they had been erected before Brown’s arrival. Most obviously related to them are the Five-Arch and Palladian bridges. If you sit at either of the temples and look out, you will see as fi ne an example of Claudean geometry as you are ever likely to see, each with a middle ground clump set on a pudding basin of a mound (Figure 5).

The South Tuscan was referred to by Thomas Whately in his 1771 account:

the setting sun shoots its last gleams on a Tuscan portico, which is close to the great basin, but which from a seat near this river is seen at a distance, through all the obscurity of the wood, glowing on the banks, and refl ected on the surface of the water.41

It has a sight line to the Palladian Bridge,42 while the Five-Arch Bridge shows just left of the shrub mound in the view from the North Tuscan.

At both Croome and Wotton we seem to have the same pattern: the composition of views from the house required a geometric design from which a number of other compositions were spun, each with its own geometrically derived setting. Each of these has some traits in common but a consciously distinct character, i.e. the views from each viewpoint are constructed quite differently from the views from any other

9PROJECTIVE GEOMETRY

viewpoint. One can get a long way by explaining the geometry of Croome and Wotton in terms of the composition of views. However, it is replicated elsewhere in ways that cannot have had much to do with views.

B U RT O N C O N S TA B L E, E A S T Y O R K S H I R E

One persuasive example of geometry that seems to go beyond the creation of views is to be found at Burton Constable, East Yorkshire, where Brown worked from c.1760–82. The principal approach there comes off the Sproatley road, past the farm, across some open pasture with ridge and furrow in good condition and makes its way to the Triumphal Arch (or Old Lodge as it is called), built after Brown, but very much in his tradition and in a place determined by him.

We may readily discern the geometric alignments that framed the layout and it is easy to distinguish those that must have predated Brown (the south, east and west avenues) and concentrate on those that appear to have had some bearing on the Brown-period

Figure 4. The geometry west of the house at Wotton House, Buckinghamshire, is as complete as Croome’s, and a straight line, parallel to the west front of the house, links the classical deities:

Venus (the Rotunda), Mars and Jupiter. Drawing: author

10 GARDEN HISTORY 34 : 1

landscape. The most striking of the latter runs north from Old Lodge to Walton’s Clump. This ‘Chinese’ line links no less than seven mid-eighteenth-century (that is Brownian) features (Old Lodge itself, the bridge between the Menagerie Pond and Long Stank, the island in Menagerie Pond, the menagerie, the octagonal shade, the ice house and the Keeper’s Lodge in Walton’s Clump).43 Framed by the arch then there would have been a grand composition, taking in the house across Long Stank and all the interest and bustle of the menagerie with its collection of birds, squirrels, tortoises, etc.,44 and Walton’s Clump, which may also have had its attractions.

The view here now requires a constructive imagination for Old Lodge has found new life as the entrance to a caravan site and the vigorous beech hedges around that deny a view of the house, let alone the lake and bridge. Nonetheless, it seems unlikely that all these structures would have been visible through the arch.

While the point of such views may deserve further consideration, more immediately relevant are the additional and still more surprising facts that the line at Burton Constable is within 0.5° of being parallel to the South Avenue and hence square to the West, and that the positions of all seven features along the line were determined by projective geometry (Figure 6).45

S I X U S E S F O R G E O M E T RY

Geometry, as has already been suggested, can make a place easier to comprehend, but there seems to be a further six possible explanations for this complexity in the design: aggrandisement – a geometry that springs from the house and is a statement of power and magnifi cence; ‘Claudean geometry’, which is an incidental consequence of making views from the front of the house that though individually asymmetrical are mirror images of each other and so create a broad symmetry; ‘engineer’s geometry’, which is simply an effi cient tool of construction (like Claudean geometry, a pragmatic application);

Figure 5. Wotton: the two Tuscans have almost identical views. The same horse chestnut frames the foregrounds, two identical shrub mounds on the Plain determine the middle ground, and in both the more distant view is to a bridge. In both views the shrub mounds are on the left of the sight line. At Croome, in the same way long reaches of the river follow the right-hand-side of

the sight lines to the Obelisk and Owl House. Drawing: author

11PROJECTIVE GEOMETRY

‘traditional geometry’, which is the unthinking use of a skill passed down from gardener to gardener; ‘plain geometry’, which is geometry for the fun of it, for no other reason; and ‘meaningful geometry’, which springs from the enlightened rationalism of the early eighteenth century and may be either Platonic (that in a perfect world everything would be perfectly ordered) or masonic (that in a perfectly ordered world, everything will be perfect). Of these options, only three will fi t Croome.

The idea of landscape as aggrandisement fi nds a place in John Claudius Loudon’s

Figure 6. The projective geometry at Burton Constable, East Yorkshire, is as impressive as it is convincing. Drawing: author

12 GARDEN HISTORY 34 : 1

infl uential theory that grand and explicitly formal designs were intended to display man’s control over nature at a time when the countryside itself was full of wildness. But since no one has hitherto noticed the geometry of Croome, if it was intended to aggrandise the place, one might say that it was wholly unsuccessful.46 If Brown had intended to aggrandise his client, he might have had quicker results if he had stuck to avenues.47

The geometry is not simply Claudean either, because it determined the position of buildings without necessarily affecting the composition of views.

Engineer’s geometry has a head start as an explanation of what Brown was doing because, as with Brownian geometry, the mechanisms devised by engineers are not usually visible or immediately comprehensible to the onlooker. In the mid-eighteenth century mathematics still provided the standard way of interpreting three-dimensional visual effects, and although the argument has been questioned, landscapers were likely to have been conservative (they want to choose plants that will grow rather than take risks with new introductions), and so were likely to regard mathematics as a reliable way of solving practical problems of design. For engineer’s geometry is immediately practical: the engineer will use geometry to give stability to a building, and a building that has geometry and symmetry will be more easily erected because its plans will be more easily understood by the builders.

It is worth observing too that at its best Brown’s operation will have relied on a good deal of three-way correspondence and communication between the client, Brown’s foreman and Brown himself. The notebooks kept by McLeish, Loudon’s foreman at Stradsett, Norfolk, some twenty-fi ve years after Brown’s death, provide an excellent record of this relationship.48 These refer to weekly letters from Loudon to the foreman, and additional correspondence with the client. In such situations a shared understanding of working rules and standards (such as mathematics can establish) would have helped Brown to work as widely over England and Wales as he did, entrusting so much to his foremen, and achieving such a constant standard of work.

One great shortcoming of this theory is that there are, as far as I know, no such records from Brown’s practice. One might argue that one should not expect to fi nd them if Brown operated something like a guild and did not want his clients, or anyone else, to know of its secrets and its mathematics, and that his foremen might have been instructed to return their records to Brown, who then destroyed them.49 This seems far-fetched. Nonetheless, the complete disappearance of the correspondence is puzzling.

A second shortcoming, as shall be shown, is that some of the geometry found in Brown’s landscapes seems unnecessary even within the context of a shared understanding of the rules of design. However, one might explain such geometry with the argument that Brown used geometry in every element of his design without asking himself why because that was the tradition in which he had been trained.

Cook, John James, Batty Langley, Switzer – writers of the garden textbooks that head-gardeners in Brown’s time would have had on their shelves – all had substantial sections devoted to geometry. Peter Collinson’s obituary letter (3 July 1742) praised the great Robert Edward, 9th Lord Petre, not only as a gardener, but also as ‘a great mechanic, as well as a great mathematician; ready at fi gures and calculations – and elegant in his tastes’.50 Brown cannot have trained as a gardener without acquiring this skill. He must have known how to set out parterres and avenues, ovals and ellipses, to fi nd a straight line through dense woodland, and even if he had wanted to set it aside, it may be doubted that he would have been able to. Each of his designs might contain

13PROJECTIVE GEOMETRY

amusement, philosophy, agriculture and other delights in varying proportions, but in each case, in whatever he did, Brown reached fi rst and instinctively for geometry to give himself a solution. Still this is not quite satisfactory: the geometry in those manuals was metrical, and ‘traditional geometry’ does not get to the heart of those cases classed above as ‘amusing’ or ‘clever’, i.e. ‘plain geometry’.

P L A I N G E O M E T RY

The ‘Chinese’ line at Burton Constable suggests a trick brought off because it was so clever (the Grand Canal at Vaux-le-Vicomte is as much of a surprise and similarly witty) and for no other reason. It encourages me to think of Brown as inventing or developing a language for landscape that was suffi ciently sophisticated to allow irony, such as might be exhibited by the geometry of the Croome Rotunda and the Windmill Hill at Wotton.

There is an anomaly in the geometry of the fi rst of these: none of the other garden buildings is visible from the centre of the Rotonda.51 This cannot be chance, for they were perfectly visible from the Rotunda site (both from the terrace outside and from the edges of the room).52 It has to have been a conscious decision because while the geometry of Croome’s layout might demand an octagonal building with views to the house, the obelisk (mentioned in 1765), London Lodge (rebuilt by Adam 1778–79) and (eventually) the Worcester Cross, the Rotunda is actually hexagonal, with fi ve windows and a door set at equal intervals around its circumference: its views were carefully composed to avoid buildings and to give views of irregular nature.

The paradox inherent in the idea of having a building in a landscape that did not actually provide views to that landscape has a crude but playful kind of wit to it. Something similar can be seen in the iconography of the north front at Croome, which set the cold ice house against the hot temple/greenhouse, the Christian church against the pagan deities, both sets of views bisected by point blank, and there is the same playfulness in the way the ridge and furrow in front of the stables at Burton Constable was modifi ed to make a lawn of lozenges, invisible in the main views, but leaping into rhythmic billowy forms at sunset.

But there is a further anomaly in the Croome Rotunda: not only is it a hexagon instead of an octagon, but also the geometrically perfect site for the building would have been approximately 70 metres further north, in line with the east axis of the house itself (Figure 7). Such a position could have picked up lines at 45° to the London Lodges, the Owl House, the obelisk and the house. The Burton Constable design, as has already been mentioned, is also offset from the house, and to these can be added the Turkey Building (known as the Turk) at Wotton, the octagonal plan of which was stretched and twisted from its geometrically ‘true’ position, so as to create a triptych with a perfect Claudean view to the lake and Rotunda with vignettes between the half-sides of the octagon to the grotto and ‘Poplar Urn’ (Figure 8).

This play with geometry has its merits – the hexagonal design of the Croome Rotunda enabled it to be built off its ‘true’ geometric position, and so superimposes a second layer of meaning on the geometric base. As for the Wotton Turk, there is no fi ner composition in Brown’s oeuvre than the sunlit Rotunda, a temple to Venus and sensual pleasure, framed by death, gloom and introspection.

In the octagon at Wotton, on the other hand, one can see the point at which projective geometry becomes destructive of good design. It has sight lines to structures of one kind or another in the middle of an astonishing seven of its eight arches, but to achieve this it

14 GARDEN HISTORY 34 : 1

Figure 7. Croome: the narrow lines show how an octagon built on the site of the Rotunda would just miss a number of the surrounding structures, and yet is close enough to them to offer

itself as the obvious design. The broad lines show that a point some 70 metres north would have given a still better fit. Drawing: author

15PROJECTIVE GEOMETRY

was necessary to add a mound only 50 metres from the South Boathouse (itself buried in a mound) on the Warrells (Figure 9). If the geometry is not perfect, and you then draw lines on a plan and place a structure at every intersection, and then draw a second set of lines to join every structure and place additional structures at their intersections, etc., the landscape will develop an infi nite number of these structures as well as problems with scale (because something that needs to be 30 feet high to be seen at a distance may only need only to be 10 feet from a closer viewpoint). If the masterpiece that is Wotton has a fault, then this is where it lies.

M E A N I N G F U L G E O M E T RY

We have thus far given no space to ‘meaningful geometry’. Brown might have been persuaded by the theories of freemasonry. This topic has already been investigated by Anne and Pal van Ypersele de Strihou and Wim Oers on Laeken (known to Brown as Schoonenberg), now the Royal Palace at Brussels.53 To summarize their brilliant analysis, Brown’s plan of 1782 was adapted in the execution (in particular, some of the buildings were moved further away from the house) so as to make the house and landscape conform to the principles of freemasonry. In short, while his design employed projective geometry and revolved around point blank, it was not masonic.

On the other hand, there is something tempting in the more Platonic belief that there is an ideal form that is inherent in the land, that has shaped perceptions for thousands of years and that art can fi nd.54

How then does one come to an understanding of this geometry? It is something fi rst developed by painters that was then developed as a way of organizing landscape,55 as rigorous as French regularity but more fl exible, more responsive to the natural world, and to human perception: ‘Order … under the Aspect of wild freedom, and … Harmony

Figure 8. Wotton; as a complete octagon, the Turkey Building (or Turk) could successfully have picked up sight lines to the ‘Poplar Urn’, the Rotunda, the ‘Vase Mound’, Mars and Homestall (dotted sight lines). However, the designer used a half-octagon (which would have limited the

views to the first three of these), but extended the length of the main front (the north-west side) by fifty per cent, so shifting the Rotunda to the north side of the main vista, and swinging the

west sight line round from the ‘Vase Mound’ to the Grotto. Drawing: author

16 GARDEN HISTORY 34 : 1

where there is the Aspect of Confusion’.56 Brown himself must have been competent at it and found it useful not only in giving coherence to landscape, but also in constructing views, forming the structure of a landscape and, perhaps, instructing his staff. He then took it further, making puns and paradoxes, making an unspoken language of it, for those who have ears to hear.

R E F E R E N C E S

Figure 9. Wotton: the Octagon may have had designed views from a remarkable seven of its eight sides. However, the sight line to the south-east missed the Southern Boathouse and so an additional mound was built, about 50 metres away, round the corner of the Warrells. The plan

shows the rash of structures around the lakes. Drawing: author

1 For the anti-French impulse in English gardening, see John Phibbs, ‘The Englishness of Capability Brown’, Garden History, 31/2 (2001), pp. 122–40 (pp. 123, 126–7).

2 Kent’s contribution was generally

recognized even in his own day. The Hon. Daines Barrington, ‘On the progress of gardening’, Archaeologia, 7 (1782), p. 130, wrote that ‘It was reserved for Kent to realise these beautiful descriptions [namely Edmund

PROJECTIVE GEOMETRY 17

Spenser’s The Faerie Queene (London, 1579), for which Kent illustrated the 1751 edn by Thomas Birch], for which he was peculiarly adapted by being a painter; as the true test of perfection in a modern garden is, that a landscape painter would choose it for a composition’. Horace Walpole was in no doubt that Kent had invented ‘an art that realizes painting’; Isabel Chase, Horace Walpole: Gardenist, An Edition of Walpole’s ‘The History of the Modern Taste in Gardening’ [written before 1770, published in 1771, fully published in 1780] (Princeton, NJ: Princeton University Press, 1943), pp. 25ff. Walpole had recourse to this definition throughout his life: at Stowe, Buckinghamshire, in 1735: ‘Wherever you stand you see an Albano Landscape’; and in 1770, ‘a tall landscape framed by the arch and the overbowering trees’; and by the end of his life in 1792, the whole country ‘exhibits the most beautiful landscapes in the world when they are framed and glazed, that is, when you look at them through the window’; Horace Walpole’s Correspondence with Sir Horace Mann, edited by Wilmarth S. Lewis, 48 vols: vol. X (New Haven, CT, & London: Yale University Press, 1941), pp. 313–15; and vol. XXXV (London: Oxford University Press, 1955), pp. 75, 282.

3 Therefore, John Vanbrugh made a sketch of the Old Palace at Woodstock when he sought to keep it in 1709; The Complete Works of Sir John Vanbrugh, vol. IV: The Letters, edited by Geoffrey Webb (London: Nonesuch, 1927–28), p. 28; William Shenstone invented the label ‘landskip-gardiners’ to describe those who gardened by making pictures: ‘every good painter of landskip appears to me the most proper designer’; William Shenstone, The Works in Verse and Prose of William Shenstone Esq., 2 vols (London: R. & J. Dodsley, 1764), II, p. 139; and William Cowper used ‘landscape’ to mean ‘painting’: ‘Estates are landscapes gaz’d upon a while/ Then advertised, and auctioneer’d away’; William Cowper, The Task …, 6 bks (London: J. Johnson, 1785), III, ll.755–6.

4 For the great value put on painting itself, see Oliver Goldsmith, ‘The Citizen of the World’ [letter XXXIV], Public Ledger (6 May 1750).

5 Revd Joseph Spence, Observations, Anecdotes, and Characters of Books and Men Collected from Conversation, edited by James M. Osborn (Oxford: Clarendon, 1966), I, p. 423 (no. 1122). In 1734 Pope had given Spence the famous dictum ‘all landscape gardening is landscape painting’ as he looked through the gate of the Oxford Botanics at ‘the view through it, that looks so much like a picture hung up’; ibid., I, p. 252 (no. 606).

6 Bishop Richard Hurd, Letters on Chivalry and Romance (London: A. Millar, 1762), p. 67.

7 This notion – to be found in Vitruvius’ De architectura libri decem (first century BC) and revisited by Leon Battista Alberti’s De re aedificatoria (written 1452, fully published Florence, 1485), and by numerous others since – tends to propose that beautiful forms are derived from measurements taken from parts of the human body: the thumb, the inch; the palm, the foot; the pace, the yard, and so on.

8 Thomas Burnet, The Sacred Theory of the Earth (London: R. Norton, 1681–89), and discussed in Basil Willey, The Eighteenth-Century Background. Studies on the Idea of Nature in the Thought of the Period (Harmondsworth: Penguin, 1965), pp. 33–6. Also Jacques Boyceau, Traité du jardinage selon les raisons de la nature et de l’art … (Paris: M. Vanlochom, 1638), and discussed by Heinz-Joachim Müllenbrock, ‘The “Englishness” of the English landscape garden and the genetic role of literature: a reassessment’, Journal of Garden History, 8/4 (1988), pp. 97–103 (p. 98). Although this idea was entirely out of keeping with Lockean philosophy, Joseph Addison, with his preference for ‘anything that hath such a variety or regularity as may seem the effect of design in what we call the works of chance’, can be said to have shared John Dryden’s view that ‘God’s first idea’ was regular. Dryden maintained that it was the role of the artist ‘imitating the Divine Maker … to Correct and amend the common Nature, and to represent it as it was first created without fault’; Charles Alphonse du Fresnoy, De arte graphica: The Art of Painting by with Remarks … Translated … by Mr. Dryden, 2 pts (London, 1695), Preface, p. v. Similarly, Timothy Nourse, ‘Essay of a country-house’, in Campania Fœlix; or, a Discourse of the Benefits and Improvements of Husbandry … (London: Thomas Bennet, 1700 edn), p. 2, at the beginning of the century described vegetable cultivation as a ‘Restauration of Nature’ and ‘a New Creation of things’. In the notes added to The Dunciad, vol. IV, ll.488–9 in 1741, Pope referred to Ashley Cooper, 3rd Earl of Shaftesbury’s, neo-classical philosopher, Theocles, who had invoked the ‘Genius of the Place’ to obtain ‘at least some faint and distant view of the Sovereign Genius and first beauty’ of ‘glorious Nature’.

9 John Ray, The Wisdom of God Man Manifested in the Works of the Creation … (London: Samuel Smith, 1691), as discussed by Willey, Eighteenth-Century Background, p. 39.

10 ‘Fabriques should bee regular, so Gardens should bee irregular, or at least cast into a very wilde Regularitie’, they should be viewed ‘rather in a delightfull confusion, then with any plaine distinction of the pieces’; Sir Henry Wotton, The Elements of Architecture ... (London: 1624); repr. with Introduction and Notes by Frederick Hard (Charlottesville, VA:

18 GARDEN HISTORY 34 : 1

University Press of Virginia for the Folgar Shakespeare Library, 1968), p. 109. In a rather difficult passage cited by Peter H. Goodchild, ‘“No Phantasticall utopia, but a reall place”. John Evelyn, John Beale and Backbury Hill, Herefordshire’, Garden History, 19/2 (1991), pp. 105–27 (p. 108), Sidney argued that in Kalander’s garden, art would make order in confusion ‘by counterfeiting his enemy Error’; Sir Philip Sidney, The Countess of Pembroke’s Arcadia (London, 1655), bk 1, p. 8.

11 Sir William Temple, ‘Upon the Gardens of Epicurus: or, of Gardening, in the year 1685’, in Miscellanea, pt II (1692); repr. in idem, The Works of Sir William Temple, Bart. …, 4 vols (London: J. Brotherton, 1770), III, pp. 229–30.

12 Pope wrote Windsor Forest (1713) to celebrate the Treaty of Utrecht and hence the English nation, and described Windsor as ‘not Chaos-like … but … harmoniously confused,/ Where order in variety we see,/ And where, though all things differ, all agree’ ll.13–16. Also Stephen Switzer, Ichnographia Rustica, Or the Nobleman, Gentleman, and Gardener’s Recreation, 3 vols (London: D. Browne, 1718), I, pp. xxxvii–xxxviii; and Joseph Addison, The Spectator, No. 414 (25 June 1712).

13 Letter from John, Viscount Perceval, to Daniel Dering (14 August 1724), BL Add. MS 47030, Egmont papers, ff.156–9; repr. George Clarke (ed.), Descriptions of Lord Cobham’s Gardens at Stowe 1700–1750 (Buckingham: Buckinghamshire Record Society, 1990), pp. 14–17.

14 ‘The 12 acres … is more diversified and of greater variety than anything of that compass I ever saw; and this method of gardening is the more agreeable, as when finished, it has the appearance of beautiful nature’; letter from Sir Thomas Robinson to Charles Howard, 3rd Earl of Carlisle (23 December 1734), Historical Manuscripts Commission, The Manuscripts of the Earl of Carlisle Preserved at Castle Howard. 15th Report, Part IV (London, 1897), VI, pp. 13–14.

15 Robert Castell, The Villas of the Ancients Illustrated (London, dated 1728, published posthumously 1729), p. 116.

16 Hurd, Letters on Chivalry and Romance, p. 67.

17 John Hill (ed.), Eden; or, a Compleat Body of Gardening … (London, 1757), p. 609.

18 Francis Hutcheson the Elder, An Inquiry into the Original of Our Ideas of Beauty and Virtue … (London, 1725), pp. 37–8.

19 When Thomas Whately, Observations On Modern Gardening, Illustrated by Descriptions (London: T. Payne, 1770), pp. 136–7, came to distinguish art and nature in his discussion of the proper setting for a building, he chose the words ‘regularity’ and ‘design’. However, his argument is unusually difficult to follow.

20 William Mason, The English Garden,

3rd edn (London: J. Dodsley, 1778), bk I, ll.308–18. Edmund Burke and Samuel Coleridge both used ‘mechanick’ in just the same way. See, for example, Burke’s famous panegyric to Marie Antoinette, ‘Reflections on the Revolution in France’, in The Works of the Right Honourable Edmund Burke (London: F. & C. Rivington, 1803–27), V, p. 152: ‘On the principles of this mechanick philosophy, our institutions can never be embodied, if I may use that expression, in persons; so as to create in us love, veneration, admiration, or attachment …’; and Samuel Coleridge, Lectures 1808–1819 on Literature, edited by R. A. Foakes, 2 vols (Princeton, NJ: Princeton University Press, 1987), I, p. 358. See also the criticism of Bridgeman’s work at Stowe in the anonymous The Rise and Progress of the Present Taste in Planting Parks, Pleasure Grounds, Gardens, &c. from Henry the Eighth to King George the Third. In a Poetic Epistle to the Right Honourable Charles Lord Viscount Irwin (London: C. Moran, 1767), in which the poet acknowledged Bridgeman’s ‘great design’, but argued that: ‘Could he have dropped the dangerous Rule and Line,/ Then Stowe had been with nobler wildness graced,/ And shown the full result of genuine taste …./ But nothing looks so miserably vile,/ As a dull regularity of style’. I suspect there is some apprehension of a shift in the basis of mathematical design in comments such as Uvedale Price’s ‘Formerly, every thing was in squares and parallelograms; now every thing is in segments of circles, and ellipses’; Uvedale Price, Essays on the Picturesque, as Compared with the Sublime and the Beautiful, 3 vols (London: Mawman, 1810 edn), I, pt 2, p. 230.

21 Pascal’s symmetry was to become ‘balance’ for Shenstone; Shenstone, The Works in Verse and Prose of William Shenstone Esq., II, p. 133.

22 Jane Brown, The Pursuit of Paradise: A Social History of Gardens and Gardening (London: HarperCollins, 1999), p. 146, reckons that land-surveying with a theodolite was mastered in England ‘from about 1540’.

23 See inter alia Peter Aram, ‘The Practical Making and Management of Gardens’ (c.1729), cited in George Sheeran, Landscape Gardens in West Yorkshire 1680–1880 (Wakefield: Wakefield Historical Publications, 1990), p. 23; Batty Langley, New Principles Of Gardening: Or, The Laying out and Planting Parterres, Groves, Wildernesses, Labyrinths, Avenues, Parks, &c. …, 7 pts (London, 1728), which begins with surveying and geometry, and idem, Practical Geometry Applied to the Usefull Arts of Building, Surveying, Gardening and Mensuration, 4 pts, 2nd edn (London, 1729), p. 33; and Switzer, Ichnographia Rustica, II, pp. 1–134.

24 Cook worked with Desgots and Hugh

PROJECTIVE GEOMETRY 19

May at Windsor Castle, Berkshire – Jane Roberts, Royal Landscape: The Gardens and Parks of Windsor (New Haven, CT, & London: Yale University Press, 1997), p. 262 – and at Cassiobury, Hertfordfshire, assuming that Samuel Richardson meant Desgots: ‘[the] large Wood-Walks … were planted by the famous Le Nôtre…’; Daniel Defoe, A Tour Thro’ the Whole Island of Great Britain, 3 vols, edited by Samuel Richardson (London, 1748 edn), II, p. 176.

25 Cook and Le Nôtre seem to have had a broadly similar attitude to nature, for it would be quite wrong to assume that Le Nôtre’s layouts themselves were purely geometrical. Still today, if one wants to find what is natural and wild at the Château de Versailles, near Paris, one has only to lose oneself in one of the many compartiments beside the main axes of the design, and a convincing case for his deployment of the genius loci has been put by Thierry Mariage, The World of André Le Nôtre, trans. Graham Larkin (Philadelphia, PA: University of Pennsylvania Press, 1999), ch. 3. Descriptions of French parks and gardens before 1700 can sound very English, as Sir Charles Somerset found of the Château de Madrid, outside Paris, built in 1528 by François I: ‘there is a parke walled rounde of some 2. English miles, wherin hertofore deere have bene, but now there is none’; The Travel Diary (1611–1612) of an English Catholic, Sir Charles Somerset, edited by Michael G. Brennan (Leeds: Leeds Philosophical and Literary Society, 1993), p. 80.

26 Moses Cook, The Manner of Raising, Ordering, and Improving Forrest Trees … (London: Peter Parker, 1676), pp. 143ff.

27 ‘… I cut a straight Line through the Wood walk at Cashiobury, from the North front, over one wall and several hedges, neer a mile long, and when I came to stake it out true, there was at the very end not four foot difference, as the ingenious Hugh May Esq; can witness, and several others’; ibid., p. 138.

28 As Humphry Repton put it in his Red Book for Higham, Essex (February 1794), ‘When the art of gardening was directed by line and rule, it was easy to lay down upon paper such a map as might be followed implicitly in the execution’.

29 In the eighteenth century wooden splines were also used; Thomas Page, The Art of Shooting Flying … (Norwich: J. Crouse, 1766), p. 11.

30 Humphry Repton, Red Books for Finedon, Northamptonshire (3 May 1793) and Wimpole Hall, Cambridgeshire (October 1801).

31 Hill, Eden, p. 55; Thomas Breaks, A Complete System of Land-Surveying … (London: J. Murray, 1778); Humphry Repton, Fragments on the Theory and Practice of Landscape Gardening ... (London, 1816);

repr. in Landscape Gardening and Landscape Architecture of the Late H. Repton, Esq., edited by John C. Loudon (London, 1840), p. 485; Leonard Meager, The English Gardener … (London, 1683), pl. 2., cited in Todd Longstaffe-Gowan, The London Town Garden 1740–1840 (New Haven, CT, & London: Yale University Press for The Paul Mellon Center for Studies in British Art, 2001), p. 111, who gives an excellent account of the method.

32 Switzer’s commendation of Bridgeman (‘now deservedly advanc’d to be one of His Majesty’s Gardeners’) for his use of the spirit-level makes a telling contrast between the methods of Bridgeman and Kent; Stephen Switzer, An Introduction to a General System of Hydrostaticks and Hydraulicks, Pholosophical and Practical, 2 vols (London, T. Astley, 1729), p. 91.

33 Richard Bradley condemned ‘Modern Designs’ where ‘fine irregular Spots of Ground, which in themselves had ten thousand Beauties, are brought to a Level at an immense Expense … in such a Case, the Surveyors do … themselves a diskindness’. He instead praised the gardens of ‘the Earl of Burlington’s at Chiswick, where the Contrivance and Disposition of the Several Parts, sufficiently declare the grand Taste of the Master …’; Dr Richard Bradley, Survey of the Ancient Husbandry and Gardening (London: B. Motte, 1725), pp. 359–61.

34 See, for example, ‘The most is made of inequalities of ground, as well as of the existence of springs, to create sheets of water, not by digging out the bed they should occupy, but by raising a dike at the interior extremity of the valley, an excellent means, which diminishes the expense, and gives a natural and graceful form to those vast reservoirs the sides of which are adorned with fine trees’; Charles Lemercher de Longpré, Baron d’Haussez, Great Britain in 1833, 2 vols (London, 1833), II, pp. 59–60. This is, of course, itself a misleading simplification.

35 For plans and William Woollett’s engraved illustration, see David Coombs, ‘The garden at Carlton House of Frederick Prince of Wales and Augusta Princess Dowager of Wales: bills in their household accounts 1728 to 1772’, Garden History, 25/2 (1997), pp. 153–77 (pp. 162, 164).

36 The avenue is partly shown on John Doharty’s plan (c.1751), and Camilla Beresford tells me that a section on Cubs Moor is shown, or referred to, on another plan. In addition, the Ordnance Survey plan of 1884 shows fragmentary lines of trees along its route. As regards field evidence, one lime from this avenue seems to survive in West Field and some grand earthworks on the way up to Cubs Moor suggest that an effort was made to cut the avenue into the hill by means of a rather

20 GARDEN HISTORY 34 : 1

crude step-like excavation (this earthwork does not look Brownian, but the Windsor vista at Langley, Buckinghamshire, was cut in an equally crude way). Cubs Moor itself was acquired in 1773, and had a mill house and new dairy in the 1780s; Richard Lockett, A Survey of Historic Parks and Gardens in Worcestershire (Hereford and Worcester: Hereford and Worcester Gardens Trust, 1997), p. 76. Almost all the documentary material from which this account is derived comes from Beresford and is now held by the National Trust.

37 For another typical example, the complex ha-has east and west of the house at Appuldurcombe, Isle of Wight, incorporating as they do waterworks and sunk roads, are both roughly 350 yards from the house.

38 Hal Moggridge’s analysis of the geometry in Brownian design is well exemplified in his seminal chapter entitled ‘Capability Brown at Blenheim’, in Blenheim Landscape for a Palace, edited by James Bond and Kate Tiller (Gloucester: Alan Sutton and the Oxford University Department for External Studies, 1987).

39 The progress of the design is recorded on two plans in the Buckinghamshire County Record Office, BAS 95/47 87, 88. The first is dated 1649 and shows the major east–west axis. Additional work was probably carried out by George London – George Clarke found a letter of 1711 from Richard Grenville querying London’s bill in the Stowe papers at Huntington Library, California; he told Dorothy Stroud and thence it came to me. Payments of 1 guinea were made to Brown in 1742, 1744 and 1746; however, he was working there as a contractor from 1757 to 1759; Benjamin Read continued until 1761, and it might be reasonable to assume that Brown continued to visit at least until the death of George Grenville in 1770.

40 The Warrells is a lake of some antiquity, probably expanded to something like its present size c.1700 by London and Wise.

41 Thomas Whately, Observations On Modern Gardening, p. 87.

42 A picture in the grangerized copy of Daniel Lysons, Magna Britannia …, Vol. I, Part 3: Buckinghamshire (London: Cadell & W. Davies, 1813), kept at the Getty Collection, Wormsley, shows a view of one of the mounds from the north shoulder of the Warrells, and there is also a view from the North Tuscan itself.

43 This is the kind of effect described by Sir William Chambers, A Dissertation on Oriental Gardening … (London: Dodsley, 1773), pp. 82–3: ‘There are … in most of the Chinese Gardens, particular places, consecrated to scenes of an extraneous nature; from whence all, or the greatest part of the buildings are

collected into one view; rising above each other in amphitheatrical order … and, by their whimsical combinations, exhibiting the most magnificent confusion imaginable’. The Keeper’s Lodge is shown on the 1755 survey (I have never visited Burton Constable at a season when the clump was accessible, for it now lies in a vast undulating range of arable land, and therefore cannot comment as I would like on the remains of the building there – whether it was substantial enough to have been ornamented, whether it included a parlour for the reception of the gentry, etc.); the menagerie by Thomas Knowlton was completed in 1763; the island, on the line of the Roe Hill Avenue, was probably land left unexcavated when the Menagerie Pond was dug in the 1770s; and the bridge was finished in 1780, which places the completion of this ‘Chinese’ line late in Brown’s career. Vanbrugh’s Grand Bridge (1706–12, 1716–24) at Blenheim has a construction line running through it at right angles to point blank, and not far from Burton Constable his Castle Howard also has ‘Chinese’ lines. Thus, the New River Bridge (1740) lies between the house and Hawksmoor’s Mausoleum (built 1731–36, completed 1742); the North Parade has Vanbrugh’s Obelisk (1714), the anonymous fountain in Wray Wood, and Hawksmoor’s Temple of Venus/Diana (built 1735); and the Great Avenue, of course, has a long sequence of incidents by both Vanbrugh and Hawksmoor along it, including the Carrmire Gate (late 1720s or c.1730), the mock fortifications/bastioned walls/castellated towers (1719–25), the Pyramid Gate (1719), as well as the Double C Bridge, the Obelisk Ponds, and the Northern Gatehouse.

44 Ivan Hall and Elizabeth Hall, Burton Constable Hall: A Century of Patronage (Hull: Hull City Museums, 1991), p. 50.

45 The geometry is derived by dropping a perpendicular from the menagerie to the line of the South Avenue. This line is, therefore, parallel to point blank but passes immediately north of the house, perhaps to the Roman Catholic chapel. The other structures (island and octagonal shade, bridge and ice house, Old Lodge and Walton’s Clump) are at angles bisected by this line. However, the distances between them are not equal (a consequence of the 0.5° difference in angle between the ‘Chinese’ line and the South Avenue). So, for example, the shade and Keeper’s Lodge are 1231 yards apart, but the Old Lodge and island are only 1136 yards.

46 There may have been some recognition of the formality of Brown’s designs in Barrington’s acknowledgement, ‘On the Progress of Gardening’, p. 130, that Brown had ‘great merit in laying out pleasure grounds’, but that, ‘I conceive that in some of his plans I see rather traces of the gardener of Old Stowe, than of

PROJECTIVE GEOMETRY 21

Poussin or Claude Lorraine’.47 Aggrandisement was emphatically a

French contribution to gardening, and for that very reason one might expect it to have been despised by the eighteenth-century English. Adam Smith – in The Theory of Moral Sentiments (London: A, Miller, 1759) and An Inquiry into the Nature and Causes of the Wealth of Nations … (London: W. Strahan & T. Cadell, 1776) – had assumed that ambitious men sought wealth in order to be noticed, but however true his observation, the Roundhead/Cavalier split in the English personality is an old one. William Harrison, Description of England (London, 1586), bk I, ch. 18, p. 109, had noticed of the new builders that ‘Each one desireth to set his house aloft on the hill, to be seen afar off, and cast forth his beams of stately and curious workmanship into every quarter of the country’, but no sooner had he published than Francis Bacon questioned the wisdom of this aspiration: ‘when man sought to cure mortality by fame … buildings were the only way’; Francis Bacon, Gesta Grayorum (London, 1594), cited in James Spedding, The Letters and Life of Francis Bacon, 7 vols (London: Longmans, 1861–72), I, p.336. And Pope was openly to mock it: ‘Who but must laugh, the master when he sees,/ A puny insect shivering at the breeze!/ Lo, what huge heaps of littleness around!/ The whole a laboured quarry above ground …’; Alexander Pope, An Epistle to the Right Honourable Richard, Earl of Burlington, Occasion’d by his Publishing Palladio’s Designs of Baths, Arches, Theatres, &c. of Ancient Rome (London, 1731), ll.107ff. Close as it is to Switzer’s criticism of Bridgeman for ‘aiming at an incomprehensible Vastness’, with his lakes ‘which he generally designed so large, as to make the whole Country look like an Ocean’ (Switzer, Ichnographia Rustica (1742 edn), I, ‘Proemial Essay’, p. 11), Pope’s lines have been taken as a description of Canons or Blenheim. They would have fitted Versailles much better, and indeed the poem sprang to Thomas Gray’s mind when he visited the French palace in 1739 and dismissed it (‘what a huge heap of littleness!’); The Poems of Mr Gray, to which are Prefixed Memoirs of his Life and Writings by W. Mason, 2 vols (Dublin: D. Chamberlaine, 1776), I, p. 55. His contemporary James Thomson described French gardens as ‘disgraceful piles of wood and stone;/ Those parks and gardens, where, his haunts betrimmed,/ And Nature by presumptuous Art oppressed,/ The woodland Genius mourns’; James Thomson, Liberty

(London, 1734–36), bk V.48 These fascinating notebooks remain at the

house.49 There may be support for the idea of a

trade secret in the outlying towers at Croome (Pirton Tower, c.1797; Baughton Hill Tower, early nineteenth century; Broadway Tower, 1799–1805; the Panorama, 1801–07) all of which are known to be James Wyatt’s or are attributed to him. As I have noted, none of their locations was derived from projective geometry. One has to conclude either that Lord Coventry’s taste had changed, or that he and Wyatt knew nothing about the underlying design of the park and that it was indeed a secret that Brown had kept to himself.

50 William Darlington, Memorials of John Bartram and Humphry Marshall with Notes of their Botanical Contemporaries, Introduction by Joseph Ewan (New York, NY: Hafner, 1967), p. 158.

51 The Rotunda is one building for which there is neither date nor designer. Its design looks too good for Brown, unless he copied it from someone else. It was built between 1756 and 1765, and modified after 1778, but its site, scale and orientation, and hence all the great outline of its design, must have been determined at an early stage. Wyatt’s Panorama tower, which is in view on Cub’s Moor, was not begun until 1801.

52 William Dean, Historical and Descriptive Account of Croome d’Abitot, the Seat of the Right Hon. the Earl of Coventry; with Biographical Notices of the Coventry Family: to which are Annexed an Hortus Croomensis, and Observations on the Propagation of Exotics (Worcester: T. Eaton, 1824), p. 63, is ambiguous. He concentrates on the natural landscape ‘rich, diversified, extensive, and well-combined’ and the only buildings he mentions are ‘the ruins of Dunstal Castle … the Saxon Tower [i.e. Broadway Tower], at Spring Hill … the Church of Strensham …’.

53 Anne van Ypersele de Strihou and Pal van Ypersele de Strihou, Laeken un château de l’Europe des Lumières (Brussels: Duculot, 1991).

54 John Phibbs, ‘Recording what isn’t there: three difficulties with 18th century landscapes’, in There by Design: Field Archaeology in Parks and Gardens, edited by Paul Pattison (Oxford: Royal Commission on the Historical Monuments of England, 1998), pp. 27–31.

55 Alberti regarded geometry as the first requirement of the painter.

56 See note 17.