The Kaleidoscope as a Design Tool: Brewster on Architectural Ornament, Painting and Carpets
Sir David Brewster did not present the kaleidoscope only as an instrument of amusement. In his book "The Kaleidoscope: Its History, Theory, and Construction, with its Application to the Fine and Useful Arts" he gives a full chapter to its use as a working tool for designers, and a second chapter to recording its patterns with a camera. This article reports what those chapters say: Chapter XIX on the number of possible patterns, Chapter XX on the fine and useful arts, and Chapter XXI on photographic delineation.
Statements about Brewster's views are taken from those chapters and carry the chapter number. The last section is a separate reading by a practising architect. Background: History of the Kaleidoscope.
Chapter XIX: how many patterns the instrument can form
Chapter XIX is short. Brewster starts with a calculation that was current in his time: by the ordinary rules of combination, twenty-four pieces of glass can be arranged 1,391,724,288,887,252,999,425,128,493,402,200 ways.
He then rejects the figure - not as too large, but as too small. The calculation assumes that one piece of glass gives one figure. In the instrument, a single object can sit at any distance from the centre of the aperture, at any angle to the radii of the field, and in any position parallel to a radius. His conclusion is that a single line, or a single piece of coloured glass with an irregular outline, already yields an unlimited number of figures.
The practical point for a designer is in the last lines of the chapter. With loose objects a figure that has been lost cannot be recalled. If the objects have very little freedom in the cell, a figure close to the earlier one can be recovered. If the objects are fixed, the same pattern returns on every revolution of the object-plate.
Chapter XX: the argument for a design instrument
Brewster opens Chapter XX with a general claim: objects of art derive their beauty from symmetry. He names one exception: the irregular forms of picturesque landscape.
His second argument is about labour. He compares the kaleidoscope to production machinery that shortens manual work, and writes: "It will create, in a single hour, what a thousand artists could not invent in the course of a year".
His third argument is about prediction. A designer who draws a symmetrical ornament does not see the result until it is complete, and cannot foresee how it will read in coloured material or in stone. Brewster states that the instrument shows the final effect, because it works from the actual materials and actual relief.
Section 1 of Chapter XX: architectural ornaments
Brewster's rule for buildings is that nearly every public and private edifice consists of two halves, one the inverted image of the other, and that doors and windows repeat this. From this he derives a requirement: borders, circular patterns and groups of figures should be symmetrical in themselves and also symmetrically related to the line that bisects the building.
Procedure for carved ornament. The architect cuts the elements of several patterns into the surface of a large stone, or places them on it in relief. The stone is set vertically and lit obliquely. The instrument, fitted with its lens tube, is placed opposite the stone at a distance that corresponds to the pattern size required, and focused so that an image of the stone forms at the end of the reflectors. The designer then shifts the instrument, turns it about its axis and varies the inclination of the reflectors.
In Brewster's words: "The architect has therefore only to select from the profusion of designs which are thus presented to him". The selected design is copied photographically, by eye, or with the Camera Lucida. Alternatively, the projection of the angular aperture is traced on the stone itself.
Mirror angle and repetition. For a natural object such as a leaf, Brewster gives a numerical rule. If the leaf is symmetrical, only half of it is carved, and the reflectors are set at an angle contained in the circle twice as many times as the leaf is to be repeated: six leaves need 1/12 of 360 degrees, which is 30 degrees. A leaf with two dissimilar halves must be applied whole, at 60 degrees for six repeats.
Gothic windows and ceilings. For circular Gothic windows he recommends applying the instrument to a mullion drawn on paper with part of the intended curves, or to ornamental parts of a drawing of a Gothic cathedral. Plaster ceiling decorations follow the same method. The word "rosette" does not occur in these chapters.
Section 2 of Chapter XX: ornamental painting
Stone and plaster ornament involve form only. Painted ornament involves form and colour together, and Brewster assigns the instrument a double task: "While it creates the outline, it at the same time fills it up with colour".
For public halls and galleries his position is that history paintings on a ceiling conflict with the symmetry of the room, and that regularly combined groups of figures are the appropriate ornament.
Procedure for figures. A single figure on a printed plate is isolated with a paper mask and viewed through an instrument whose mirror inclination does not exceed 30 degrees. Figures larger than the aperture are reduced with the lens. His Fig. 51 was made at 36 degrees, 1/10 of a circle, so the object appears ten times as five pairs of direct and inverted images.
Section 3 of Chapter XX: designs for carpets
Brewster states that no useful art is more directly suited to the instrument than carpet manufacture, because the manufacturer needs a design complete with its colours. He describes a carpet as a number of kaleidoscope designs arranged in lines parallel to the sides of the room, related to the shape of the apartment.
Shape of the field. The outline is set by the line that bounds the field at the wide end of the angular aperture. His rules:
A circular bounding line gives a circular field.
A square field: mirrors at 45 degrees with the line perpendicular to one reflector, or mirrors at 90 degrees with the line equally inclined to both.
A triangular field: mirrors at 60 degrees with the line perpendicular to one reflector, or mirrors at 120 degrees.
Selection of colour. The worsteds intended for production, preferably already woven into cloth, are laid on a flat surface a few feet from the instrument, and their image is formed at the end of the reflectors by the lens. Moving the instrument changes which colour predominates and how the masses of colour are placed.
Other trades. At the end of the chapter Brewster lists the further users he expects: the jeweller arranging stones, the bookbinder, the wire-worker, the paper-stainer, and the maker of painted glass windows.
Chapter XXI: recording the pattern with a camera
Brewster calls the earlier methods - the ground glass of a camera obscura, or a camera lucida at the eye end - very imperfect. Patterns copied for use were generally drawn by a draughtsman who delineated one sector and repeated it.
Photography - he names the Daguerreotype and Talbotype processes - changes this. With a Kaleidoscope Camera, figures are transferred to paper or plated copper, and he expects "hundreds of designs offered to the choice of the artist who is to employ them".
Optical arrangement. A small achromatic lens of rock crystal or glass, a quarter of an inch in diameter, is placed in contact with the eye end of the reflectors. If its focal length equals half the length of the instrument, the image forms at the size of the object-box.
Camera. Any photographic camera can be adapted by removing its own lens and fixing the kaleidoscope in the sliding tube.
Light and objects. Sunlight falling obliquely on the object-box is preferred; coal gas, Bengal lights, lime-ball light and the Bude light are listed as substitutes. Red, orange and dark yellow objects are to be avoided because they transmit few actinic rays. Pale blue, pale green and pale yellow glass combined with colourless glass are recommended.
External objects. For flowers, plants, architectural ornaments, paintings, photographs or statues he specifies the telescopic kaleidoscope. With the common instrument the figure depends on chance; external objects can be grouped and lit deliberately. See What Is a Teleidoscope.
What maps to current practice: an architect's reading
This section is my own reading, not Brewster's text.
Pattern generation from a small unit. Brewster's method is: define one sector, let reflection produce the whole, change the sector, inspect again. This is the same logic as drawing one unit in CAD and applying mirror and rotational array operations.
Symmetry groups. The angle rules in Chapter XX are statements about what mathematics now calls dihedral symmetry: two mirrors at 360/2n degrees give n mirror axes and n-fold rotation. Repeating plane patterns - tiles, perforated screens, facade panels - are classified into 17 wallpaper groups, a classification proved in 1891, after Brewster's death in 1868. Squares and equilateral triangles, his two polygonal fields, both tile a plane without gaps. The three-mirror arrangements are described in Two-Mirror vs Three-Mirror Kaleidoscope.
Testing in the real material. Viewing the actual stone relief and the actual worsted corresponds to the sample panel and mock-up stage in building practice.
What does not transfer. His rule that all building ornament must follow the axis of the building is an aesthetic position of his period, not a technical requirement. His forecast of wide adoption across trades is a prediction; I have not verified how far any trade adopted it. Related reading: An Architect Reads the Kaleidoscope and Kaleidoscopic Architecture.
Checklist: using a kaleidoscope for pattern study
Use fixed or nearly fixed objects if a pattern has to be recalled (Chapter XIX).
Choose the mirror angle by the number of repeats: angle = 360 degrees / (2 x repeats) for a half-motif.
Put the actual material in front of the instrument, not a drawing of it.
Light the object obliquely if relief has to read.
Record the selected pattern at once, by photograph.
FAQ
What does Brewster say about the kaleidoscope in architecture?
In Chapter XX, Brewster proposes that an architect carve pattern elements on a stone, light it obliquely and view it through a kaleidoscope with a lens. He also recommends the instrument for circular Gothic windows, applied to a mullion drawn on paper, and for plaster ceiling decoration.
How many patterns can a kaleidoscope produce according to Brewster?
Chapter XIX quotes a contemporary calculation of about 1.39 x 10^33 arrangements for twenty-four pieces of glass. Brewster calls this figure too small. He argues that one object alone, even a single line, forms an unlimited number of figures, because its distance, angle and position in the aperture can vary continuously.
How did Brewster propose to use the kaleidoscope for carpet design?
Chapter XX, Section 3, instructs the manufacturer to lay the coloured worsteds, preferably woven into cloth, a few feet from an instrument fitted with a lens. Moving the instrument changes the outline and the proportion of each colour. A square field is obtained with mirrors at 45 or 90 degrees.
Which trades did Brewster expect to use the kaleidoscope?
Chapter XX names the architect, the ornamental painter, the plasterer and the carpet manufacturer in its three sections. Its closing paragraph adds five more: the jeweller arranging stones, the bookbinder, the wire-worker, the paper-stainer and the maker of painted glass windows.
How did Brewster record kaleidoscope patterns photographically?
Chapter XXI describes a Kaleidoscope Camera. A lens a quarter of an inch in diameter is placed at the eye end of the reflectors, and the instrument is fixed in the sliding tube of a camera. The image forms on the ground glass and is taken on collodion or paper.
What mirror angle repeats a motif six times?
By Brewster's rule in Chapter XX, a symmetrical motif such as a leaf is carved as one half and viewed with reflectors at 30 degrees, which is 1/12 of 360 degrees. The whole leaf viewed at 60 degrees gives the same six-fold figure. An asymmetrical leaf must be applied whole.Part of the series: Brewster's kaleidoscope book - reading guide. The instrument: the Architect's Edition Kaleidoscope.
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