The Telescopic Kaleidoscope: Brewster's 1858 Chapter That Describes the Teleidoscope

5 days ago

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The word "teleidoscope" does not appear in Sir David Brewster's book. The instrument does. Chapter X of "The Kaleidoscope: Its History, Theory, and Construction" (second edition, London, John Murray, 1858) is titled "On the construction and use of the telescopic kaleidoscope, for viewing objects at a distance". It describes a mirror system with a lens in front of it, pointed at the surroundings instead of at an object cell.

This article reads that chapter as a technical document: the defect Brewster was correcting, the lens arrangement he specified, how he used it, and what still applies to a teleidoscope built today with a lens or a glass sphere.

The problem: the simple kaleidoscope only works at the end of the reflectors

Chapter X opens with a test. Brewster takes a simple kaleidoscope, holds the object box against the reflectors and then withdraws it. At one-tenth of an inch (about 2.5 mm) the pattern begins to distort at the centre, because the reflected images no longer join. The distortion spreads outward, and at eighteen inches (about 46 cm) or less, in his words, "all the symmetry and beauty of the pattern will disappear".

The reason is given earlier, in Chapter V, which deals with the position of the object. Brewster examines three cases:

Object inside the reflectors. The picture is symmetrical, but its centre does not coincide with the centre of the luminous field, so the result is an eccentric pattern inside a circular field. The object also cannot be moved, so the pattern cannot be varied.

Object in the plane of the mirror ends. The images of the object are similarly disposed in all sectors. This is the working position.

Object beyond the mirror ends. Symmetry is lost. Brewster's explanation links to Chapter IV, on the position of the eye: the eye is necessarily a little above the line where the two mirrors meet, so it looks through the aperture at a part of the object lying below the mirror planes. The directly seen sector then no longer matches its first reflections, and every later reflection inherits the mismatch.

The conclusion is geometric: a mirror kaleidoscope has one object plane, at the end of the reflectors.

Brewster's solution: move the image, not the object

A distant tree cannot be brought to the end of the mirrors. Its image can. Brewster places a lens, either single or achromatic, in front of the aperture at a distance that forms an image of the distant object at the mirror ends. He reports that the image formed by the lens then behaves as a new object and is multiplied by successive reflections in the same manner as a physical object placed there.

For the general mirror geometry behind this, see how a kaleidoscope works.

The construction Brewster specifies

Chapter X calls the instrument the Compound or Telescopic Kaleidoscope, and in one passage the Tele-Kaleidoscope. The construction, as described in the chapter:

Two tubes. An inner tube carries the reflectors. An outer tube carries the lens at its far end. Sliding the inner tube changes the lens-to-mirror distance, which is the focus adjustment.
Removable lens. The lens and its mount can be taken off and replaced with the object cell. With the inner tube pushed fully in, the instrument works as a simple kaleidoscope.
Focal length. It should be much less than the length of the outer tube, and in general such that an image forms at the mirror ends when the tube is fully extended and the object is three or four inches (about 8-10 cm) from the lens.
Lens diameter. Brewster treats this as the critical dimension. If the lens is too small, the brass rim holding it becomes the edge of the field. The centre of the pattern then no longer coincides with the centre of the field, the outline of the field breaks into disconnected curves, and in bad cases a dark spot appears at the centre.

What to check, in Brewster's own procedure: remove the eye-glass, set the lens at its greatest distance, and look through. If the rim of the lens mount is visible, the lens is too small.

How Brewster says the instrument should be used

The operating sequence in Chapter X is short:

Remove the object cell and fit the lens.
Direct the instrument at the subject.
Draw the inner tube out until the inverted images are distinct. Brewster equates sharp focus with correct symmetry: when the image is in focus, it lies in the object plane.
Vary the pattern by turning the instrument round its axis and by moving it across the subject.

For a subject about four inches from the lens the tube is fully extended. For greater distances it is pushed in. He notes that most instruments carry a mark near the middle of the tube that suits nearly all distances beyond three feet (about 0.9 m).

For calibration he gives a test target: a straight line, set at an inclination to the line bisecting the mirror angle. When the reflected images of the line join exactly into a star or polygon, the tube is at the correct length for that distance.

What Brewster recommends viewing

The list in Chapter X is specific: the furniture of a room, books and papers on a table, pictures on a wall, a fire, moving branches and foliage, bunches of flowers, horses and cattle in a park, carriages in motion, river currents, waterfalls, moving insects, and the sun shining through clouds or trees. He closes the list with "every object in nature may be introduced by the aid of the lens into the figures created by the instrument".

Two points in this list are technical rather than descriptive.

Motion comes from the subject. Brewster writes: "Here the objects are independent of the observer". In a simple kaleidoscope the user moves the object cell. In the telescopic instrument the subject moves by itself and the mirror system repeats that motion in every sector.

Position accuracy improves. In a simple kaleidoscope the objects have thickness and sit behind a glass plate, so they are never exactly in the object plane. Brewster notes that the compound instrument is free of this error, because an image has no thickness and can be formed in the mathematical position of symmetry.

How this relates to the teleidoscope

A teleidoscope is a mirror system with a front optic and no object cell. That is the instrument of Chapter X with the object cell left off. The differences are in the front optic and in the focusing.

Front optic - Brewster, Chapter X (1858): Lens, single or achromatic, removable; Teleidoscope today: Lens, glass sphere, or both
Focus - Brewster, Chapter X (1858): Sliding inner tube, marked scale; Teleidoscope today: Usually fixed
Object cell - Brewster, Chapter X (1858): Interchangeable with the lens; Teleidoscope today: None

A glass sphere is a lens with a very short focal length. For glass with a refractive index near 1.5, the effective focal length of a sphere is about 0.75 of its diameter, measured from its centre. The image of a distant scene therefore forms close behind the sphere, and the position of that image changes little between a subject at a few metres and one at the horizon. This is why a sphere can be used at a fixed distance from the mirrors, without Brewster's sliding tube.

Brewster already describes the fixed-lens variant, and not favourably. In a footnote to Chapter X he mentions a Paris instrument with a lens fixed about two inches in front of the reflectors. It gives symmetrical pictures at one distance only and cannot be used as an ordinary kaleidoscope. His verdict: "It is merely the Telescopic Kaleidoscope deteriorated."

On the question "who invented the teleidoscope": the principle and a complete construction are in Brewster's Chapter X. A United States patent titled "Telescopic kaleidoscope" (US 3,661,439) was filed in 1970 and granted on 9 May 1972 to John L. Burnside III and Henry Hay. It describes an objective lens with an added converging lens between it and the mirrors, to even out illumination of the image.

For a side-by-side comparison of the two instrument types, see kaleidoscope vs teleidoscope and what is a teleidoscope.

What has changed since 1858, and what has not

Not changed: the object plane is still at the end of the mirrors, the front optic still has to be large enough that its mount does not become the edge of the field, and the pattern is still varied by rotating the instrument and sweeping it across the subject.

Changed:

Mirror type. A front-surface mirror carries its reflective coating on the face of the glass, so light does not pass through the glass and no second reflection forms at the glass surface. Chapter X does not specify the reflector material. The book's Chapter XI covers instruments with metallic and with glass reflectors.
Front optic. The glass sphere has joined the lens as a front optic, and the two can be combined.
Focus. Most current teleidoscopes are fixed-focus. Brewster's sliding tube and distance scale are rarely built.
Mirror count. Chapter X is written around a pair of reflectors with an angular aperture. Three-mirror systems, which Brewster treats separately in Chapter XIII, are common in teleidoscopes today. See two-mirror vs three-mirror kaleidoscopes.

Checklist: testing a teleidoscope by Brewster's criteria

Point it at a straight edge set at an angle, such as a window frame. The reflected segments should join into a closed star or polygon without steps at the joints.
Check the centre of the pattern. It should coincide with the centre of the bright field.
Check the edge of the field. It should be a continuous outline, not disconnected arcs.
Look for a dark spot at the centre. Brewster attributes it to a front optic that is too small.
Test at two distances, about 1 m and beyond 10 m. Note whether the joints stay closed at both.
Rotate the instrument and sweep it across a moving subject, such as foliage in wind. Both should change the pattern.
Check which front optic is fitted: lens, sphere, or both.

FAQ

What is a telescopic kaleidoscope?

It is the instrument Sir David Brewster describes in Chapter X of his 1858 book: a kaleidoscope mirror system with a lens mounted in a sliding outer tube. The lens forms an image of a distant subject at the end of the reflectors, and the mirrors repeat that image. Brewster also calls it the Compound Kaleidoscope.

Who invented the teleidoscope?

Brewster published the principle and a full construction in Chapter X of "The Kaleidoscope: Its History, Theory, and Construction" (second edition, 1858), under the name telescopic kaleidoscope. A United States patent with the same title, US 3,661,439, was granted on 9 May 1972 to John L. Burnside III and Henry Hay.

Why does a simple kaleidoscope fail with distant objects?

Brewster's Chapter V shows that symmetry requires the object to lie in the plane of the mirror ends. In Chapter X he reports that distortion starts at the centre when the object is one-tenth of an inch away, and that at eighteen inches or less the symmetry of the pattern is gone.

How did Brewster focus the telescopic kaleidoscope?

The reflectors sit in an inner tube that slides inside the outer tube holding the lens. The user draws the tube out until the inverted images are sharp. For a subject about four inches from the lens the tube is fully extended. A mark near mid-tube suits distances beyond three feet.

What did Brewster recommend viewing through it?

Chapter X lists room furniture, books and papers on a table, pictures on a wall, a fire, moving foliage, flowers, horses and cattle, carriages in motion, river currents, waterfalls, moving insects, and the sun through clouds or trees. He notes that moving subjects transfer their motion to every sector of the pattern.

Is a glass sphere teleidoscope different from Brewster's design?

The principle is the same: a front optic forms an image at the mirror ends. A glass sphere with a refractive index near 1.5 has a focal length of about 0.75 of its diameter, so the image forms close behind it and the instrument can work at fixed focus, without Brewster's sliding tube.

About Studio Yabaye

Studio Yabaye builds kaleidoscopes and teleidoscopes with front-surface mirror systems in a brass tube, cut, fitted and hand-finished in the studio. The Studio Yabaye Teleidoscope combines both front optics discussed above, a lens and a glass sphere, with a three-mirror system, and it works in every light condition except indoor artificial lighting. The studio is based in Israel and ships worldwide. The current range is at all products, and questions can be sent through the contact page.