Before Brewster: Porta, Kircher, Bradley and the Mirrors That Were Not a Kaleidoscope

3 days ago

11 min read

By Rocco (Roi) Ramon - licensed architect, founder of Studio Yabaye

Two plane mirrors hinged along one edge multiply whatever stands between them. That arrangement was in print long before David Brewster patented the kaleidoscope in 1817. When the patent was copied, the older books were used as the argument that nothing new had been invented. The question "who invented the kaleidoscope" therefore depends on what counts as a kaleidoscope.

This article goes through the earlier devices one by one, using Brewster's own review of them in "A Treatise on the Kaleidoscope" (Edinburgh, 1819), Chapter XVIII and the Appendix. In the enlarged 1858 edition the same history is Chapter XXIII. The three conditions he tests the older devices against are stated in the opening history chapter of the same book. One caution applies to everything below: this is Brewster's account, written by the patentee while his patent was under attack. The older texts are reported here as he quotes and translates them. The wider timeline is in the history of the kaleidoscope.

The definition that produced so many inventors

Brewster opens Chapter XVIII with the definition his critics used: an instrument of two reflectors that multiplies objects, wherever the objects are placed and wherever the eye is. Under that definition, he writes, the candidates are without number. He lists them: anyone who had watched a fire repeated between two polished plates of brass or steel, anyone who had dressed between a pair of looking-glasses, every jeweller who set two upright mirrors in a shop window to multiply the goods between them, and every toy-maker who built reflecting show-boxes.

Giambattista della Porta: the polyphaton

Brewster names Baptista Porta as the earliest writer he found who described the use of two plane mirrors. Brewster places the passage in Book VII, Chapter 2 of Magia Naturalis. In the twenty-book edition of 1589 and its 1658 English translation, the mirror chapters are in Book XVII, "Of Strange Glasses", Chapters 2 and 3. Brewster prints the Latin from an Amsterdam edition of 1664 and gives his own literal translation.

The device. Two rectangular mirrors of brass or crystal stand on one base. Their length is one and a half times their width, or any other proportion. They are joined along one long side so that they open and shut like a book. Porta calls it a polyphaton, a speculum that shows many objects.

What it did. A face or a finger held in front of the pair is multiplied. The closer the mirrors are shut, the more images appear. Opened to an obtuse angle, they show fewer. Porta reports twenty and more images of a single finger.

Not Porta's own. Porta says such mirrors were commonly made at Venice. In his next chapter he attributes a multiplying speculum built of plane mirrors to the ancients, citing writings that circulated under Ptolemy's name. He then describes his own show-box: ten mirrors in a polygonal arrangement with one side open, holding small columns, pictures, gems, pearls and coloured birds.

Brewster's reply. Porta lets the mirrors stand at any angle, because multiplication works at every angle. A symmetrical picture was not the purpose. Brewster's verdict is that Porta's instruments "have no farther connection with the Kaleidoscope than that they are composed of plane mirrors". Of the ten-mirror box he says that its effect comes only from the accumulation of individual images.

Athanasius Kircher: mirrors on a divided semicircle

The second candidate is Kircher. Brewster quotes Ars Magna Lucis et Umbrae (Rome, 1646), where Kircher presents the behaviour of the hinged pair as a property that, as far as he knew, nobody had observed.

The device. The same two mirrors, opening like a book, are set upright on a sheet on which a semicircle is divided into degrees. The hinge stands on the centre. The angle can therefore be read off.

What it did. Kircher records what appears at each opening. Brewster rearranges the passage as a table:

180 degrees - one image and one object
120 degrees - two images and one object
90 degrees - four images
72 degrees - a pentagon and five forms
60 degrees - a hexagon and six forms
45 degrees - an octagon and eight forms
36 degrees - a decagon and ten forms
30 degrees - a dodecagon and twelve forms

The table also includes the settings for seven, nine and eleven sides. Kircher states the general rule: the polygon has as many sides as the number of times the mirror angle is contained in 360 degrees.

This claim has more technical content than Porta's. The rule that links angle to the number of repeats is the one every two-mirror kaleidoscope still follows, as explained in kaleidoscope mirror angles. Brewster concedes the point. He writes that Porta only noted that the images increase as the angle closes, while Kircher showed the relation between the number of images and the inclination of the mirrors.

Brewster's reply. He makes three objections.

Kircher's aim was to repeat a figure that was already regular. Brewster marks odd divisions in the table with an asterisk and notes that Kircher did not see that at those angles the last two reflected images do not unite, unless a regular object is placed symmetrically to both mirrors.
The eye was in front of the mirrors. The object was much nearer the eye than its images, so the reflected sectors differed in brightness and in apparent size.
The object was lines on paper. That choice hid the distortion. Applied to the loose objects of a kaleidoscope, Brewster says, the same pair of mirrors could not produce its forms.

As evidence he cites Schott (Magia Universalis Naturae et Artis, Würzburg, 1657), who repeats Kircher's description almost word for word and adds that the mirrors also multiply distant objects, such as a wall with windows, into a large public place lined with buildings. Brewster invites the reader to try it: the result is heaps of windows and walls of unequal size, distance and brightness, none of them joined.

Richard Bradley, 1717: a tool for garden plans

The third candidate is Richard Bradley, in New Improvements of Planting and Gardening, which Brewster dates to 1717. Bradley became Professor of Botany at Cambridge in 1724, and Brewster refers to him by that title. Brewster quotes his instructions at length.

The device. Two pieces of looking-glass of equal size, five inches long and four inches broad, backed with paper or silk to protect the silvering, and hinged to open like the leaves of a book.

What it did. Bradley used it as a design aid.

Draw a circle on paper, divide it into three, four, five, six, seven or eight equal parts, and draw part of a garden plan in one division.
Stand the mirrors on the two lines that bound that division. The whole circular plan appears, for example six parts with six walks leading to a hexagonal basin at the centre.
Fix the mirrors at a right angle and slide them over a drawing. A circle can be shown as an oval and a square as a long rectangle.
Slide the same right-angled pair over a deliberately irregular plate, with scales on its four sides for reference. Bradley counts at least two hundred different plans from one plate no larger than a hand.

What Brewster grants. He does not accuse Bradley of copying Kircher, or Kircher of copying Porta. He thinks the apparatus was forgotten between one author and the next, and that each added something. He also says Bradley made the apparatus worse by making the mirrors wider than they are high. Bradley's addition, he says, was noticing that figures with some irregularity could still form a regular design.

Brewster's reply. Four numbered conclusions:

Bradley allows the third, fifth and seventh part of the circle. He therefore did not know that the angle must be an even aliquot part for an irregular object to form a complete figure.
The eye is in front of the mirrors. The light of the reflected sectors is so unequal that the last one is hardly visible.
For the same reason the sectors differ in apparent size. Brewster points out that Bradley uses this as a feature, to turn a circle into an oval.
The sectors are separated by a gap equal to the thickness of the glass plates, and reflections from the first surface overlap those from the second.

Harris and Wood: theorems without an instrument

Brewster says that Kircher's and Bradley's mirrors had been known to opticians for so long that works on optical instruments had stopped mentioning them. The critics therefore turned to two textbooks.

Wood's Optics, Propositions XIII and XIV. These calculate the number and arrangement of images formed by two reflectors, inclined or parallel. Brewster's objection is that they assign no position to the eye or the object and say nothing of the alternation of direct and inverted images.

Harris's Optics, Proposition XVII and its scholia. Harris's propositions deal with the multiplied sectors and the path of a ray between two mirrors. Brewster notes that the eye is never mentioned in the propositions on the sectors, that in Proposition XVII the eye and the object are both placed between the reflectors, and that Harris treats odd and even divisions of the circle as equivalent. The only practical device Harris describes is a box of four mirrors holding upright figures, of a kind known long before.

The three conditions Brewster uses as the test

Against every earlier device Brewster applies the three conditions he sets out in the history chapter that opens the Treatise.

Angle. The inclination of the mirrors must be an aliquot part of the circle - an even part for irregular objects. An odd part works only for an object placed symmetrically to both mirrors.
Object position. The object must be in contact with the ends of the mirrors, so that it joins its own reflections without a step. For distant objects he obtains the same result with lenses.
Eye position. The eye must be close to the angular point, at the opposite end of the mirrors. From there the symmetry is complete and the light of the circular field is as uniform as the arrangement allows.

In Chapter XVIII he states that the positions of the eye, the mirrors and the object, so far as he knew, had not been investigated by any author. He adds a separate claim: even with the theory known, building an instrument that met the conditions took further work.

How contemporaries judged it: the Appendix

The Appendix prints four opinions. Brewster says why he includes them: many readers lack the optical knowledge to follow the comparison, and the subject would soon come before a tribunal other than the public. The letters were collected for a dispute.

Wood. In a note dated St John's, 19 May 1818, replying to Brewster's direct question, Professor Wood writes that his propositions are a mathematical calculation only: "The effects produced by the Kaleidoscope were never in my contemplation."

Watt. James Watt, in an undated letter, reports the rumour that Brewster took the idea from an old book on gardening. He obtained Bradley's book in a London edition of 1731, describes the two hinged glasses, five inches long and four inches high, and says he saw such an instrument in his father's possession seventy years earlier. His conclusion: "In my opinion, the application of the principle is very different from that of your Kaleidoscope."

Playfair. John Playfair, Professor of Natural Philosophy at Edinburgh, writes on 11 May 1818 that he compared the instrument with Bradley's and with Wood's propositions. Bradley and Wood, he says, go no further than multiplying the figure. The kaleidoscope needs a particular position of eye and object: "If either of these is wanting, the symmetry vanishes, and the figures are irregular and disunited." A postscript adds two features he regards as peculiar to Brewster: coloured, movable objects at the end of the reflectors, and two lenses with a draw-tube for distant objects.

Pictet. M. A. Pictet, Professor of Natural Philosophy in the Academy of Geneva, writes that he saw the patent infringed in London, and that he found nothing resembling the instrument in the French, German or Italian optical authors he knew, nor in Professor Charles's collection of optical instruments in Paris.

All four letters support Brewster. He selected them, and at least one was requested by him. They show that four named scientists accepted his distinction. They do not show what his opponents answered.

A fair assessment

What was old:

Two plane mirrors hinged at a variable angle - in print with Porta, and according to Porta made at Venice before him.
The rule that the number of repeats equals 360 degrees divided by the angle - stated by Kircher in 1646.
The use of the pair to generate design variants from a drawing - Bradley, 1717.

What the earlier texts, as quoted, do not contain:

A distinction between even and odd divisions of the circle.
A fixed eye position at the angular point.
An object plane at the mirror ends, holding loose objects in motion.
A requirement for reflection from a single surface.
An enclosed tube that fixes all of these at once.

Inclined mirrors were old. The symmetrical instrument with defined conditions was new. Brewster's tone is that of an advocate, but the technical distinction can be checked by anyone with two mirrors and a sheet of paper. How the copying played out is in the kaleidoscope craze.

What to check: a mirror pair against the three conditions

Reproduce Kircher. Stand two small mirrors on a drawing, hinge over the centre, and look from the front. Compare the brightness and size of the far sector with the near ones.

Move the eye. Bring the eye to the upper end of the hinge and look down along it toward the drawing. The sectors become more nearly equal in size and brightness.

Try an odd division. Set 72 degrees over an irregular scribble. Look for the joint where two sectors fail to mirror each other.

Check the surface. With ordinary back-silvered glass, look for the gap and the doubled line at each joint. A front-surface mirror reflects from one surface only and removes both.

Checklist

Device: polyphaton (Porta), mirrors on a graduated semicircle (Kircher), garden-design glasses (Bradley).
Mirror angle: free in Porta, tabulated in Kircher, any equal division in Bradley, even aliquot part in Brewster.
Eye: in front of the mirrors in all three earlier devices, at the angular point in Brewster.
Object: a face, a drawing, a distant wall - versus loose objects at the mirror ends.
Source of all quotations: Brewster, 1819, Chapter XVIII and Appendix. The three conditions: the opening history chapter.

FAQ

Who invented the kaleidoscope?

David Brewster patented the kaleidoscope in 1817 and described it in his 1819 Treatise. Hinged plane mirrors that multiply an object are older: Brewster himself cites Porta, Kircher in 1646 and Bradley in 1717. His claim covers the instrument that fixes the mirror angle, the object position and the eye position to give symmetry.

Was there a kaleidoscope before Brewster?

By Brewster's definition, no. His 1819 Treatise reviews earlier pairs of hinged mirrors described by Porta, Kircher and Bradley, and argues that none fixed the three conditions for symmetry. By the looser definition used by his critics - any two mirrors that multiply an object - the device was already old when Porta described it.

What did Kircher's mirrors do?

In Ars Magna Lucis et Umbrae (Rome, 1646), as quoted by Brewster, Kircher stood two hinged mirrors on a semicircle divided into degrees. He recorded the figure at each angle: a hexagon at 60 degrees, an octagon at 45, a dodecagon at 30. The polygon has as many sides as the angle divides into 360.

What was Bradley's 1717 instrument?

Richard Bradley, later Professor of Botany at Cambridge, described two hinged looking-glasses, five inches by four, in New Improvements of Planting and Gardening (dated 1717 by Brewster). Stood on a drawing of one division of a circle, they showed a complete garden plan. Sliding them over an irregular plate gave, by his count, at least two hundred variants.

What are Brewster's three conditions for a kaleidoscope?

First, the mirror angle must be an aliquot part of the circle, and an even one for irregular objects. Second, the object must be in contact with the ends of the mirrors. Third, the eye must be close to the angular point at the opposite end. Brewster argues that no earlier author stated them.

What did Watt and Playfair say about the dispute?

In letters printed in the Appendix of the 1819 Treatise, James Watt wrote that Bradley's hinged glasses, which he had seen seventy years earlier, applied the principle very differently. John Playfair wrote on 11 May 1818 that the kaleidoscope differed essentially from Bradley's instrument and from Wood's propositions. Brewster selected both letters himself.

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