Transcriber’s Notes:
Underscores “_” before and after a word or phrase indicate _italics_
in the original text.
Equal signs “=” before and after a word or phrase indicate =bold= in
the original text.
Small capitals have been converted to SOLID capitals.
Illustrations have been moved so they do not break up paragraphs.
Old or antiquated spellings have been preserved.
Typographical and punctuation errors have been silently corrected.
The list of works by Sir David Brewster has been moved form the first
page to the end of the text.
[Illustration]
THE KALEIDOSCOPE,
ITS HISTORY, THEORY, AND CONSTRUCTION.
WITH ITS APPLICATION TO THE FINE AND USEFUL ARTS.
BY
SIR DAVID BREWSTER, K.H., M.A., D.C.L.,
F.R.S., V.P.R.S., EDIN., M.R.I.A., F.G.S., F.R.A.S.,
ASSOCIATE OF THE IMPERIAL INSTITUTE OF FRANCE, HONORARY OR
CORRESPONDING MEMBER OF THE ACADEMIES OF PETERSBURGH, VIENNA, BERLIN,
COPENHAGEN, STOCKHOLM, BRUSSELS, GOTTINGEN, MODENA, AND OF THE
NATIONAL INSTITUTE OF WASHINGTON, AND PRINCIPAL OF THE
UNITED COLLEGES OF ST. SALVATOR AND ST. LEONARD, ST. ANDREWS.
_Nihil tangit quod non ornat._
[Illustration]
Third Edition, greatly enlarged.
WITH FIFTY-SIX WOOD ENGRAVINGS AND ONE PLATE.
LONDON:
JOHN CAMDEN HOTTEN, PICCADILLY.
1870.
CONTENTS.
PAGE
INTRODUCTION—HISTORY OF THE KALEIDOSCOPE, 1
CHAP. I.—PRELIMINARY PRINCIPLES RESPECTING THE
EFFECTS OF COMBINING TWO PLAIN MIRRORS, 9
II.—ON THE PRINCIPLES OF THE KALEIDOSCOPE,
AND THE FORMATION OF SYMMETRICAL PICTURES BY THE
COMBINATION OF DIRECT AND INVERTED IMAGES, 16
III.—ON THE EFFECTS PRODUCED BY THE MOTION OF
THE OBJECT AND THE MIRRORS, 26
IV.—ON THE EFFECTS PRODUCED UPON THE SYMMETRY OF
THE PICTURE BY VARYING THE POSITION OF THE EYE, 37
V.—ON THE EFFECTS PRODUCED UPON THE SYMMETRY
OF THE PICTURE BY VARYING THE POSITION OF THE OBJECT, 46
VI.—ON THE INTENSITY OF THE LIGHT IN
DIFFERENT PARTS OF THE FIELD, AND ON THE EFFECTS
PRODUCED BY VARYING THE LENGTH AND BREADTH OF THE
REFLECTORS, 51
VII.—ON THE CONSTRUCTION AND USE OF THE SIMPLE
KALEIDOSCOPE, 59
VIII.—ON THE SELECTION OF OBJECTS FOR THE
KALEIDOSCOPE, AND ON THE MODE OF CONSTRUCTING THE
OBJECT-BOX, 67
IX.—ON THE ILLUMINATION OF TRANSPARENT OBJECTS
IN THE KALEIDOSCOPE, 76
X.—ON THE CONSTRUCTION AND USE OF THE TELESCOPIC
KALEIDOSCOPE, FOR VIEWING OBJECTS AT A DISTANCE, 81
XI.—ON THE CONSTRUCTION AND USE OF POLYANGULAR
KALEIDOSCOPES, IN WHICH THE REFLECTORS CAN BE FIXED
AT ANY ANGLE, 88
1. Bate’s Polyangular Kaleidoscope with Metallic
Reflectors, 89
2. Bate’s Polyangular Kaleidoscope with Glass
Reflectors, 94
XII.—ON THE CONSTRUCTION AND USE OF ANNULAR AND
PARALLEL KALEIDOSCOPES, 98
1. Mr. Dollond’s Universal Kaleidoscope, 100
2. Ruthven’s Universal Kaleidoscope, 102
XIII.—ON THE CONSTRUCTION AND USE OF POLYCENTRAL
KALEIDOSCOPES, 105
1. On combinations of four mirrors forming a square, 107
2. On combinations of four mirrors forming a
rectangle, 109
3. On combinations of three reflectors at angles
of 60°, 109
4. On combinations of three reflectors at angles
of 90°, 45°, and 45°, 111
5. On combinations of three reflectors at angles
of 90°, 60°, and 30°, 112
XIV.—ON KALEIDOSCOPES IN WHICH THE EFFECT
IS PRODUCED BY TOTAL REFLEXION FROM THE INTERIOR
SURFACES OF TRANSPARENT SOLIDS, 114
XV.—ON THE APPLICATION OF THE KALEIDOSCOPE TO
THE MAGIC LANTERN, SOLAR MICROSCOPE, AND CAMERA
OBSCURA, 117
XVI.—ON THE CONSTRUCTION OF KALEIDOSCOPES WHICH
COMBINE THE COLOURS AND FORMS PRODUCED BY
POLARIZED LIGHT, 122
XVII.—ON THE CONSTRUCTION OF STEREOSCOPIC
KALEIDOSCOPES, 126
XVIII.—ON THE CONSTRUCTION OF MICROSCOPIC
KALEIDOSCOPES, 128
XIX.—ON THE CHANGES PRODUCED BY THE KALEIDOSCOPE, 131
XX.—ON THE APPLICATION OF THE KALEIDOSCOPE TO
THE FINE AND USEFUL ARTS, 134
1. Architectural Ornaments, 137
2. Ornamental Painting, 141
3. Designs for Carpets, 144
XXI.—ON THE PHOTOGRAPHIC DELINEATION OF THE
PICTURES CREATED BY THE KALEIDOSCOPE, 148
XXII.—ON THE ADVANTAGES OF THE KALEIDOSCOPE AS
AN INSTRUMENT OF AMUSEMENT, 154
XXIII.—HISTORY OF THE COMBINATIONS OF PLANE
MIRRORS WHICH HAVE BEEN SUPPOSED TO RESEMBLE
THE KALEIDOSCOPE, 162
1. Baptista Porta’s multiplying speculum, 164
2. Kircher’s combination of plane mirrors, 168
3. Bradley’s combination of plane mirrors, 175
APPENDIX, 185
ON THE KALEIDOSCOPE.
INTRODUCTION.
HISTORY OF THE KALEIDOSCOPE.
The name Kaleidoscope, which I have given to a new Optical Instrument,
for creating and exhibiting beautiful forms, is derived from the Greek
words χαλός, _beautiful_; εἶδος, _a form_; and σχοπέω, _to see_.
The first idea of this instrument presented itself to me in the year
1814, in the course of a series of experiments on the polarization of
light by successive reflexions between plates of glass, which were
published in the _Philosophical Transactions_ for 1815, and which the
Royal Society did me the honour to distinguish by the adjudication of
the Copley Medal. In these experiments, the reflecting plates were
necessarily inclined to each other during the operation of placing
their surfaces in parallel planes; and I was therefore led to remark
the circular arrangement of the images of a candle round a centre,
and the multiplication of the sectors formed by the extremities of
the plates of glass. In consequence, however, of the distance of the
candles, &c., from the ends of the reflectors, their arrangement was
so destitute of symmetry, that I was not induced to give any farther
attention to the subject.
On the 7th of February 1815, when I discovered the development of the
complementary colours, by the successive reflexions of polarized light
between two plates of gold and silver, the effects of the Kaleidoscope,
though rudely exhibited, were again forced upon my notice; the
multiplied images were, however, coloured with the most splendid tints;
and the whole effect, though inconceivably inferior to the creations
of the Kaleidoscope, was still far superior to anything that I had
previously witnessed.
In giving an account of these experiments to M. Biot on the 6th of
March 1815, I remarked to him, “that when the angle of incidence (on
the plates of silver) was about 85° or 86°, and the plates almost
in contact, and inclined at a very small angle, the two series of
reflected images appeared at once in the form of two curves; and that
the succession of splendid colours formed a phenomenon which I had no
doubt would be considered, by every person who saw it to advantage, as
one of the most beautiful in optics.” These experiments were afterwards
repeated with more perfectly polished plates of different metals, and
the effects were proportionally more brilliant: but notwithstanding
the beauty arising from the multiplication of the images, and the
additional splendour which was communicated to the picture by the
richness of the polarized tints, it was wholly destitute of symmetry,
as I was then ignorant of those positions for the eye and the objects,
which are absolutely necessary to produce that magical union of parts,
and that mathematical symmetry throughout the whole picture, which,
independently of all colouring, give to the visions of the Kaleidoscope
the peculiar charm which distinguishes them from all artificial
creations.[1]
[1] An account of the experiments above alluded to was given in
the _Analyse des Travaux de la Classe des Sciences Mathématiques
et Physiques de l’Institut Royal de France, pendant l’année 1815_,
par M. le Chev. Delambre, p. 29, &c. The colours produced by
repeated reflexions from plates of silver are those of _Elliptical
Polarization_, and are explained at great length in my paper on that
subject, published in the _Philosophical Transactions_ for 1830.
Although I had thus combined two plain mirrors, so as to produce highly
pleasing effects, from the multiplication and circular arrangement of
the images of objects placed at a distance from their extremities, yet
I had scarcely made a step towards the invention of the Kaleidoscope.
The effects, however, which I had observed, were sufficient to prepare
me for taking advantage of any suggestion which experiment might
afterwards throw in the way.
In repeating, at a subsequent period, the very beautiful experiments
of M. Biot, on the action of homogeneous fluids upon polarized light,
and in extending them to other fluids which he had not tried, I found
it most convenient to place them in a triangular trough, formed by two
plates of glass cemented together by two of their sides, so as to form
an acute angle. The ends being closed up with pieces of plate glass
cemented to the other plates, the trough was fixed horizontally, for
the reception of the fluids. The eye being necessarily placed without
the trough, and at one end, some of the cement, which had been pressed
through between the plates at the object end of the trough, appeared
to be arranged in a manner far more regular and symmetrical than I
had before observed when the objects, in my early experiments, were
situated at a distance from the reflectors. From the approximation to
perfect symmetry which the figure now displayed, compared with the
great deviation from symmetry which I had formerly observed, it was
obvious that the progression from the one effect to the other must
take place during the passage of the object from the one position to
the other; and it became highly probable, that a position would be
found where the symmetry was mathematically perfect. By investigating
this subject optically, I discovered the leading principles of the
Kaleidoscope, in so far as the inclination of the reflectors, the
position of the object, and the position of the eye, were concerned.
I found, that in order to produce perfectly beautiful and symmetrical
forms, three conditions were necessary.
1. That the reflectors should be placed at an angle, which was an
_even_ or an _odd_ aliquot part of a circle, when the object was
regular, and similarly situated with respect to both the mirrors; or
the _even_ aliquot part of a circle when the object was irregular, and
had any position whatever.
2. That out of an infinite number of positions for the object, both
within and without the reflectors, there was _only one_ where perfect
symmetry could be obtained, namely, when the object was placed in
contact with the ends of the reflectors. This was precisely the
position of the cement in the preceding experiment with the triangular
trough.
3. That out of an infinite number of positions for the eye, there was
_only one_ where the symmetry was perfect, namely, as near as possible
to the angular point, so that the circular field could be distinctly
seen; and that this point was the _only one_ out of an infinite number
at which the uniformity of the light of the circular field was a
maximum, and from which the direct and the reflected images had the
same form and the same magnitude, in consequence of being placed at the
same distance from the eye. This, also, was the position in which the
eye was necessarily placed when looking through the fluid with which
the glass trough was partially filled.
Upon these principles I constructed an instrument, in which I fixed
_permanently_, across the ends of the reflectors, pieces of coloured
glass, and other irregular objects; and I showed the instrument in this
state to some members of the Royal Society of Edinburgh, who were much
struck with the beauty of its effects. In this case, however, the forms
were nearly permanent; and slight, though beautiful, variations were
produced by varying the position of the instrument with respect to the
source of light.
The great step, however, towards the completion of the instrument
remained yet to be made; and it was not till some time afterwards that
the idea occurred to me _of giving motion to objects, such as pieces
of coloured glass, &c., which were either fixed or placed loosely in
a cell at the end of the instrument_. When this idea was carried into
execution, and the reflectors placed in a tube, and fitted up on the
preceding principles, the Kaleidoscope, in its _simple form_, was
completed.
In this form, however, the Kaleidoscope could not be considered as
a general philosophical instrument of universal application. The
least deviation of the object from the position of symmetry at the
end of the reflectors, produced a deviation from beauty and symmetry
in the figure, and this deviation increased with the distance of the
object. The use of the instrument was therefore limited to objects in
contact with the ends of the reflectors, or held close to them, and
consequently to objects, or groups of objects, whose magnitudes were
less than its triangular aperture.
The next, and by far the most important step of the invention, was
to remove this limitation, and to extend indefinitely the use and
application of the instrument. This effect was obtained by employing a
draw tube, containing a convex lens, or, what is better, an achromatic
object-glass of such a focal length, that the images of objects, of
all magnitudes and at all distances, might be distinctly formed at the
end of the reflectors, and introduced into the pictures created by the
instrument in the same manner as if they had been reduced in size, and
placed in the true position in which alone perfect symmetry could be
obtained.
When the Kaleidoscope was brought to this degree of perfection, it was
impossible not to perceive that it would prove of the highest service
in all the ornamental arts, and would, at the same time, become a
popular instrument for the purposes of rational amusement. With these
views I thought it advisable to secure the exclusive property of it
by a Patent;[2] but in consequence of one of the patent instruments
having been exhibited to some of the London opticians, the remarkable
properties of the Kaleidoscope became known before any number of them
could be prepared for sale. The sensation excited by this premature
exhibition of its effects is incapable of description, and can be
conceived only by those who witnessed it. “It very quickly became
popular,” says Dr. Roget, in his excellent article on the KALEIDOSCOPE
in the _Encyclopædia Britannica_, “and the sensation it excited in
London throughout all ranks of people was astonishing. It afforded
delight to the poor as well as the rich; to the old as well as the
young. Large cargoes of them were sent abroad, particularly to the East
Indies. They very soon became known throughout Europe, and have been
met with by travellers even in the most obscure and retired villages in
Switzerland.” According to the computation of those who were best able
to form an opinion on the subject, no fewer than two hundred thousand
instruments were sold in London and Paris during three months. Out of
this immense number there were perhaps not one thousand constructed
upon scientific principles, and capable of giving anything like a
correct idea of the power of the Kaleidoscope; and of the millions who
have witnessed its effects, there is perhaps not a hundred individuals
who have any idea of the principles upon which it is constructed, who
are capable of distinguishing the spurious from the real instrument, or
who have sufficient knowledge of its principles to be able to apply it
to the numerous branches of the useful and ornamental arts.
Under these circumstances I have thought it necessary to draw up
the following short treatise, for the purpose of explaining, in as
popular a manner as I could, the principles and construction of the
Kaleidoscope; of describing the different forms in which it is fitted
up; of pointing out the various methods of using it as an instrument
of recreation; and of instructing the artist how to employ it in the
numerous branches of the useful and ornamental arts to which it is
applicable.
[2] As this Patent, in so far as the simple Kaleidoscope is concerned,
was to a great extent infringed, it has been supposed that it was
reduced in a Court of Law. The validity of the Patent was never
questioned by any lawyer, or any philosopher acquainted with its theory
and construction, as will appear from the opinion of four competent
judges, given in the _Appendix_.
In a trial for the infringement of a Patent several years ago, a
distinguished judge (we believe it was Judge Alderson) stated it as
a fact, that the Patent for the Kaleidoscope had been set aside in a
Court of Law. The party whose case was prejudiced by this erroneous
assertion, applied to me for an affidavit, by which he was enabled to
contradict it in Court, and remove any unfavourable impression it might
have made upon the jury.
CHAPTER I.
PRELIMINARY PRINCIPLES RESPECTING THE EFFECTS OF COMBINING TWO PLAIN
MIRRORS.
The principal parts of the Kaleidoscope are two reflecting planes, made
of glass, or metal, or any other reflecting substance ground perfectly
flat and highly polished. These reflectors, which are generally made
of plate glass, either rough ground on their outer side, or covered
with black varnish, may be of any size, but in general they should be
from four or five to ten or twelve inches long; their greatest breadth
being about an inch when the length is six inches, and increasing in
proportion as the length increases. When these two plates are put
together at an angle of 60°, or the sixth part of a circle, as shown
in Fig. 1, and the eye placed at the narrow end =E=, it will observe
the opening =A O B= multiplied six times, and arranged round the centre
=O=, as shown in Fig. 2.
[Illustration: FIG. 1.]
[Illustration: FIG. 2.]
In order to understand how this effect is produced, let us take a
small sector of white paper of the shape =A O B=, Fig. 2, and having
laid it on a black ground, let the extremity =A O= of one of the
reflectors be placed upon the edge =A O= of the sector. It is then
obvious that an image =A O _b_= of this white sector of paper will be
formed behind the mirror =A O=, and will have the same magnitude and
the same situation behind the mirror as the sector =A O B= had before
it. In like manner, if we place the edge =B O= of the other reflector
upon the other side =B O= of the paper sector, a similar image =B O
_a_= will be formed behind it. The origin of three of the sectors seen
round =O= is therefore explained: the first, =A O B=, is the white
paper sector seen by direct vision; the second, =A O _b_=, is an image
of the first formed by _one_ reflexion from the mirror =A O=; and the
third is another image of the first formed by _one_ reflexion from the
other mirror =B O=. But it is well known, that the reflected image of
any object, when placed before another mirror, has an image of itself
formed behind this mirror, in the very same manner as if it were a new
object. Hence it follows, that the image =A O _b_= being, as it were, a
new object placed before the mirror =B O=, will have an image =_a_ O α=
of itself formed behind =B O=; and for the same reason the image =B O
_a_= will have an image =_b_ O β= of itself, formed behind the mirror =A
O=, and both these new images will occupy the same position behind the
mirrors as the other images did before the mirrors.
A difficulty now presents itself in accounting for the formation of the
last or sixth sector, =α O β=. Mr. Harris, in the XVIIth Prop. of his
Optics, has evaded this difficulty, and given a false demonstration of
the proposition. He remarks, that the last sector, =α O β= is produced
“by the reflexion of the rays forming either of the two last images”
(namely, =_b_ O β= and =_a_ O α=); but this is clearly absurd, for the
sector =α O β= would thus be formed of two images lying above each
other, which is impossible. In order to understand the true cause of
the formation of the sector =α O β=, we must recollect that the line =O
E= is the line of junction of the mirrors, and that the eye is placed
any where in the plane passing through =O E= and bisecting =A O B=.
Now, if the mirror, =B O=, had extended as far as =O β=, the sector =α
O β= would have been the image of the sector =_b_ O β=, reflected from
=B O=; and in like manner, if the mirror =A O= had extended as far as
=O α=, the sector =α O β= would have been the image of the sector =_a_
O α= reflected from =A O=; but as this overlapping or extension of the
mirrors is impossible, and as they must necessarily join at the line
=O E=, it follows, that an image =α O _e_=, of only half the sector
=_b_ O β=, viz., =_b_ O _r_=, can be seen by reflexion from the mirror
=B O=; and that an image =β O _e_=, of only half the sector =_a_ O α=,
viz., =_a_ O _s_=, can be seen by reflexion from the mirror =A O=.
Hence it is manifest, that the last sector, =α O β=, is not, as Mr.
Harris supposes, _a reflexion from either of the two last images_, =_b
o_ β=, =_a o_ α=, but is composed of the images of two half sectors,
one of which is formed by the mirror =A O=, and the other by the mirror
=B O=.
Mr. Harris repeats the same mistake in a more serious form, in his
second Scholium, § 240, where he shows that the images are arranged
in the circumference of a circle. The two images =D=, _d_, says he,
coincide and make but one image. Mr. Wood has committed the very same
mistake in his second Corollary to Prop. XIV., and his demonstration
of that Corollary is decidedly erroneous. This Corollary is stated in
the following manner:—“When _a_ (the angle of the mirrors) is a measure
of 180° _two images coincide_,” and it is demonstrated, that _since
two images of any object_ =X= (Fig. 2) _must be formed_, viz., one by
each mirror, and since these two images must be formed at 180° from
the object =X=, placed between the mirrors, that is, at the same point
_x_, it follows that the two images must coincide. Now, it will appear
from the simplest considerations, that the assumption, as well as the
conclusion, is erroneous. The image _x_ is seen by the last reflexion
from the mirror =B O E=, and another image _would be seen at x_, if the
mirror =A O E= had extended as far as _x_; but as this is impossible,
without covering the part of the mirror =B O E=, which gives the first
image _x_, there can be only one image seen at _x_. When the object =X=
is equidistant from =A= and =B=, then one-half of the last reflected
image _x_ will be formed by the last reflexion from the mirror =B O=,
and the other half by the last reflexion from the mirror =A O=, and
these two half images will join each other, and form a whole image at
_e_, as perfect as any of the rest. In this last case, when the angle
=A O B= is a little different from an even aliquot part of 360°, the
eye at =E= will perceive at _e_ an appearance of two incoincident
images; but this arises from the pupil of the eye being partly on one
side of =E= and partly on the other; and, therefore, the apparent
duplication of the image is removed by looking through a very small
aperture at =E=. As the preceding remarks are equally true, whatever be
the inclination of the mirrors, provided it is an even aliquot part of
a circle, it follows,—
1. That when =A O B= is ¼, ⅙, ⅛, ⅒, ¹/₁₂, etc., of a circle, the number
of reflected images of any object =X=, is 4 - 1, 6 - 1, 8 - 1, 10 - 1,
12 - 1.
2. That when =X= is nearer one mirror than another, the number of
images seen by reflexion from the mirror to which it is nearest will
be ⁴/₂, ⁶/₂, ⁸/₂, ¹⁰/₂, ¹²/₂, while the number of images formed by the
mirror from which =X= is most distant will be ⁴/₂ - 1, ⁶/₂ - 1, ⁸/₂ -
1, ¹⁰/₂ - 1; that is, an image more always reaches the eye from the
mirror nearest =X=, than from the mirror farthest from it.
3. That when =X= is equidistant from =A O= and =B O=, the number of
images which reaches the eye from each mirror is equal, and is always
4 - 1, 6 - 1, 8 - 1, 10 - 1, 12 - 1
----- ----- ----- ------ ------
2 2 2 2 2
which are fractional values, showing that the last image is composed of
two half images.
When the inclination of the mirrors, or the angle =A O B=, Fig. 3,
is an _odd_ aliquot part of a circle, such as ⅓, ⅕, ⅐, ⅑, etc., the
different sectors which compose the circular image are formed in the
very same manner as has been already described; but as the number of
_reflected sectors_ must in this case always be _even_, the line =O E=,
where the mirrors join, will separate the two last reflected sectors,
=_b_ O _e_=, =_a_ O _e_=. Hence it follows,—
[Illustration: FIG. 3.]
1. That when =A O B= is ⅓, ⅕, ⅐, ⅑, etc., of a circle, the number of
reflected images of any object is 3 - 1, 5 - 1, 7 - 1, etc., and,—
2. That the number of images which reach the eye from each mirror is
3 - 1 5 - 1 7 - 1,
-----, -----, -----,
2 2 2
which are always even numbers.
Hitherto we have supposed the inclination of the mirrors to be
_exactly_ either an even or an odd aliquot part of a circle. We shall
now proceed to consider the effects which will be produced when this is
not the case.
If the angle =A O B=, Fig. 2, is made to increase from being an _even_
aliquot part of a circle, such as ⅙th, till it becomes an _odd_
aliquot part, such as ⅐th, the last reflected image =β O α=, composed
of the two halves =β O _e_=, =α O _e_=, will gradually increase, in
consequence of each of the halves increasing; and when =A O B= becomes
⅐th of the circle, the sector =β O α= will become double of =A O B=,
and =α O _e_=, =β O _e_= will become each complete sectors, or equal to
=A O B=.
If the angle =A O B= is made to vary from ⅙th to ⅕th of a circle, the
last sector =β O α= will gradually diminish, in consequence of each of
its halves, =β O _e_=, =α O _e_=, diminishing; and just when the angle
becomes ⅙th of a circle, the sector =β O α= will have become infinitely
small, and the two sectors, =_b_ O β=, =_a_ O α=, will join each other
exactly at the line =O _e_=, as in Fig. 3.