HISTORY OF THE COMBINATIONS OF PLANE MIRRORS WHICH HAVE
BEEN SUPPOSED TO RESEMBLE THE KALEIDOSCOPE.
It has always been the fate of new inventions to have their origin
referred to some remote period; and those who labour to enlarge the
boundaries of science, or to multiply the means of improvement, are
destined to learn, at a very early period of their career, that the
desire of doing justice to the living is a much less powerful principle
than that of being generous to the dead. This mode of distributing
fame, injurious as it is to the progress of science, by taking away one
of the strongest excitements of early genius, has yet the advantage of
erring on the side of generosity; and there are few persons who would
reclaim against a decision invested with such a character, were it
pronounced by the grave historian of science, who had understood and
studied the subject to which it referred.
The apparent simplicity, both of the theory and the construction of the
Kaleidoscope, has deceived very well-meaning persons into the belief
that they understood its mode of operation; and it was only those that
possessed more than a moderate share of optical knowledge, who saw that
it was not only more difficult to understand, but also more difficult
to execute, than most of the philosophical instruments now in use. The
persons who considered the Kaleidoscope as an instrument consisting
of two reflectors, which multiplied objects, wherever these objects
were placed, and whatever was the position of the eye, provided that
it received only the reflected rays, were at no loss to find numerous
candidates for the invention. All those, indeed, who had observed the
multiplication and circular arrangement of a fire blazing between two
polished plates of brass or steel; who had dressed themselves by the
aid of a pair of looking-glasses, or who had observed the effects of
two mirrors placed upon the rectangular sides of a drawing-room, were
entitled, upon such a definition, to be constituted inventors of the
Kaleidoscope. The same claim might be urged for every jeweller who had
erected in his window two perpendicular mirrors, and placed his wares
before them, in order to be multiplied and exhibited to advantage;
and for every Dutch toy-maker, and dealer in optical wonders, who had
manufactured show-boxes, for the purpose of heaping together, in some
sort of order, a crowd of images of the same object, of different
intensities, seen under different angles, and presenting different
sides to the eye. This mode of grouping images, dissimilar in their
degree of light, dissimilar in their magnitude, and dissimilar in
their very outlines, produced such a poor effect, that the reflecting
show-boxes have for a long series of years disappeared from among the
number of philosophical toys.
From these causes, the candidates for the merit of inventing the
Kaleidoscope have been so numerous, that they have started up in every
part of the world; and many individuals, who are scarcely acquainted
with the equality of the angles of incidence and reflexion, have not
scrupled to favour the world with an account of the improvements which
they fancy they have made upon the instrument.[19]
[19] It would be an easy matter to amuse the reader with an account
of these improvements. One of the most notable of them consists
in covering the back of the reflectors with white paint, for the
purpose of increasing the light of the circular field. This scheme
is identically the same as if the author had proposed to improve the
magnificent telescopes of Herschel, when rendered dark with a high
magnifying power, by _white-washing_ the interior of the tube.
The earliest writer who appears to have described the use of two plane
mirrors, was Baptista Porta, who has given an account of several
experiments which he performed with them, in the second chapter of the
seventh book of his _Magia Naturalis_.
As the combination of plane mirrors which he there describes has been
represented as the same as the Kaleidoscope, we shall give the passage
at full length:—
_Speculum è planis multividum construere._
“Speculum construitur, quod _polyphaton_ id est multorum
visibilium dicitur, illud enim aperiendo et claudendo solius
digiti viginti et plura demonstrat simulacra. Sic igitur id
parabis. Ærea duo specula vel crystallina rectangula super
basim eandem erigantur, sintque in hemiolia proportione,
vel alia, et secundum longitudinis latus unum simul colligentur,
ut libri instar apte claudi et aperiri possint, et anguli
diversentur, qualia Venetiis factitari solent: faciem
enim unam objiciens, in utroque plura cernes ora, et hoc
quanto arctius clauseris, minorique fuerint angulo: aperiendo
autem minuentur; et obtusiori cernes angulo, pauciora numero
conspicientur. Sic digitum ostendens, non nisi digitos
cernes, dextra insuper dextra, et sinistra sinistra convisuntur;
quod speculis contrarium est: mutuaque id evenit
reflexione, et pulsatione, unde imaginum vicissitudo.”
—_Edit. Amstelod_, 1664.
The following is an exact and literal translation of this passage:—
_How to construct a multiplying speculum out of plane ones._
A speculum is constructed, called _polyphaton_, that is,
_which shows many objects_, for by opening and shutting it,
it exhibits twenty and more images of the finger alone.
You will therefore prepare it in the following manner:—Let
two rectangular specula of brass or crystal be erected
upon the same base, and let their length be one and a half
times their width, or in any other proportion; and let two
of their sides be placed together, so that they may be opened
and shut like a book, and the angles varied, _as they are
generally made at Venice_. For by presenting your face,
you will see in both more faces the more they are shut, and
the less that the angle is; but they will be diminished by
opening it, and you will see fewer as you observe with a
more obtuse angle. If you exhibit your finger, you will
see only fingers, the right fingers being seen on the right
side, and the left on the left side, which is contrary to
what happens in looking-glasses, and this arises from the
mutual reflexion and repulsion which produce a change of
the images.[20]
[20] We request that the reader will take the trouble of comparing with
the original the following translation of Baptista Porta’s description,
which was published in London, and copied into all the foreign
newspapers, etc. We hope the translator of it had no improper motive
in altering the obvious meaning of the original; yet it is singular,
that in the journal where this translation appeared, the specification
of the patent was published under the title of Directions for making
the Kaleidoscope, purporting to be an original communication to that
journal, the name of the patentee, and the technical parts of the
specification having been left out, apparently to promote the belief
that there was no patent, and that every person might make them with
impunity. The following is the translation alluded to:—
“In the following manner we may construct a mirror for seeing a
multitude of objects on a plain surface. This kind of mirror,
when constructed, is what is called _polyphaton_, that is to say,
multiplying, for by opening and shutting, it shows twenty and more
images of one single finger. If, therefore, you wish to prepare it, let
two brazen or crystal rectangular mirrors be erected on the same base,
and let the proportion of length be one and a half of the width, or any
other proportion; and let each side for the whole of its length be so
connected together that they may easily be shut and opened like a book,
and that the angles may be varied, as they are usually constructed at
Venice; for if you place _one object opposite to the face of each_,
you will see _several figures_; and this in proportion as you shut it
closer, and the angle shall be less. But, by opening, _the objects_
will be reduced in number, and the more obtuse the angle under which
you see it, the _fewer objects_ will be seen. So if you exhibit your
finger _as the object_, you will see nothing but fingers. The right
fingers will be seen on the right side, and the left on the left side,
which is contrary to the usual custom with looking-glasses; but this
happens from the mutual reflexion and repulsion which produce a change
of the images.”
It is quite obvious, from the preceding passage, that the multiplying
speculum described by Porta was not an invention of his own, but had
been long made at Venice. In the very next chapter, indeed, where he
describes a _speculum theatrale_ or _amphitheatrale_ (the _show-box_
of Harris and other modern authors), he expressly states, that a
multiplying speculum was invented by the ancients.—“Speculum autem
è planis compactum, cui si unum spectabile demonstrabitur, plura
illius rei simulachra demonstrabit, _prudens invenit vetustas_; ut ex
quibusdam Ptolemæi scriptis quæ circumferuntur percipitur;” that is, “a
speculum consisting of plane ones, which, when one object is presented
to it, will exhibit several images of it, was invented by skilful
antiquity, as appears from some of the writings of Ptolemy.” This
speculum, which consists of several mirrors arranged in a polygon, with
the object within it, is characterized by Porta as puerile, and much
less wonderful and agreeable than one of his own, which he proceeds to
describe. This new speculum consists of ten mirrors, placed within a
box, in a sort of polygonal form, with one of the sides of the polygon
open. Architectural columns, pictures, gems, pearls, coloured birds,
etc., are all placed within the box, and their images are seen heaped
together in inextricable disorder, as a whole, but so as to astonish
the spectator by their number, and by the arrangement of individual
groups. Porta speaks of this effect as so beautiful, “_ut nil jucundius
nil certe admirabilius oculis occurset nostris_,”—that nothing more
agreeable, and certainly nothing more admirable, was ever presented to
our eyes.
It would be an insult to the capacities of the most ordinary readers
to show that the instruments here described by Baptista Porta have no
farther connexion with the Kaleidoscope than that they are composed of
plane mirrors.
The sole purpose of these instruments was to _multiply_ objects by
reflexion; and so little did the idea of producing a symmetrical
picture enter into Baptista Porta’s contemplation, that he directs the
mirrors to be placed at any angle, because the multiplying property
of the mirrors is equally developed, whatever be the angle of their
inclination.
The show-box of which Porta speaks with such admiration, has so many
mirrors, and these are placed at such angles, that not one of the
effects of the Kaleidoscope can be produced from them. Its beauty is
entirely derived from the accumulation of individual images.
The next competitor for the invention of the Kaleidoscope is the
celebrated Kircher, who describes, as an invention of his own, the
construction of two mirrors which can be opened and shut like the
leaves of a book. This instrument is represented in Fig. 54, and is
described in the following passage:—
[Illustration: FIG. 54.]
PARASTASIS I.
_Specula plana multiplicativa sunt specierum unius rei._
Vide Fig. 54.
Mira quædam et a nemine, quod sciam observata proprietas elucescit in
duobus speculis ita constructis, ut ad instar libri claudi et aperiri
possint; ponantur illa in plano quopiam, in quo semicirculum in gradus
suos descriptum habeas. Si enim punctum, in quo specula committuntur,
in centro semicirculi statuas, ita ut utrumque speculi latus diametro
insistat, semel tantam videbitur rei imago, apparebuntque duæ res, una
extra speculum vera, altera intra, phantastica: Si vero specula ita
posueris, ut divaricatio laterum 120 gradus intercipiat, videbis rei
intra latera est, quia angulus reflexionis et incidentiæ tantus est,
quantus est angulus interceptus a lateribus, videlicet 120 grad. qui
cum obtusius sit, non nisi binam imaginem causare potest, ut in Propos.
v. fol. 848, ostensum est. Si vero specula interceperint angulum 90
graduum, videbis in plano circulum in quatuor partes divisum, in
quibus totidem simulacra rei positæ comparabunt, tria phantastica,
et unum verum; cum enim reflectio fiat ad angulos rectos utrumque
latus reflectens formam causabit intra se alias duas formas, unde et
consequentur pro multiplicatione laterum formæ multiplicabuntur, quæ
et in reflectione laterum normam servabunt uti in Propos. v. fol.
848, ostendimus. Porro si speculorum latera interceperint angulum 72
graduum, videbis in plano horizontali efformari perfectum et regulare
pentagonum, in quo totidem formæ apparebunt, item, si sexaginta
graduum interceperint angulum, videbis hexagonum totidemque formas
quinque nimirum phantasticas unam veram. Ita, si speculorum angulus
interceperit 51 gradus cum ³/₇ comparebit perfectum heptagonum,
cum totidem rei intra specula collocatæ formis; non secus angulus
speculorum 45 graduum dabit octogonum; 40 graduum dabit enneagonum;
36 graduum decagonum; 32 graduum angulus cum ⁸/₁₁ dabit endecagonum
et denique angulus 30 graduum referet dodecagonum cum totidem formis,
et sic in infinitum; ita ut semper tot laterum sit futurum polygonum
anacampticum totidemque formarum, quot polygonum cuivis latus
speculorum intercipit divaricatio, latera habuerit: quorum omnium
rationes dependent a Propos. v. precedentis distinctionis. —Kircheri,
_Ars Magna Lucis et Umbræ_. Rom. 1646, p. 890.
The following is a translation of the preceding passage:—
PARASTASIS I.
_Plane specula may be made to multiply the images of one object._ See
Fig. 54.
A wonderful, and, so far as I know, a new property, is exhibited by
two specula, so constructed that they may be opened and shut like a
book. If they are placed upon any plane, in which there is a semicircle
divided into degrees, in such a manner that the point where the
specula meet is in the centre of the circle, and the edge of each
speculum stands upon the diameter of the semicircle, one image only
will be visible, and there will appear two things, namely, a real one,
without the specula, and another formed by reflexion behind them,[21]
and so on, as in the following table, where the first column shows
the inclination of the specula, and the second the figure which is
produced:—
[21] I have thrown the rest of the passage into a tabular form, that
the reader may see, more readily, the effect produced by the variation
of the angle.
_Angle of Specula._ _Effect produced._
180° one image and one object,
*120° two images and one object,
90° four images,
*72° a pentagon and five forms,
60° a hexagon and six forms,
*51³/₇° a heptagon and seven forms,
45° an octagon and eight forms,
*40° an enneagon and nine forms,
36° a decagon and ten forms,
*32⁸/₁₁° an endecagon and eleven forms,
30° a dodecagon and twelve forms,
and so on, _ad infinitum_, the polygon formed by reflexion having
always as many sides as the number of times that the angle of the
specula is contained in 360°.
The combination of plane mirrors, which Kircher describes in the
preceding extract, is precisely the same as that which is given by
Baptista Porta. The latter, indeed, only mentions, that the number of
images increases by the diminution of the angle, whereas Kircher gives
the number of images produced at different angles, and enumerates the
_regular polygons_ which are thus formed.
It must be quite obvious to any person who attends to Kircher’s
description, that the idea never once occurred to him of producing
beautiful and symmetrical forms by means of plane mirrors. His _sole
object_ was to multiply a given regular form a certain number of times;
and he never imagined that, when the mirrors were placed at the angles
marked with an asterisk, there could be no symmetry in the figure, and
no union of the two last reflected images, unless in the case where
a regular object was placed, either by design or by accident, in a
position symmetrically related to both the reflectors.
In Kircher’s mirrors the eye was placed in front of them. The object
therefore was much nearer the eye than the images, and the light of
the different reflected images was not only extremely unequal, but
the difference in their angular magnitude was such that they could
not possibly be united into a symmetrical whole. From the accidental
circumstance of his using _lines upon paper_ as an object, the
distortion of the pictures arising from the erroneous position of the
eye was prevented; but if the same combination of mirrors were applied
to the object-plates of the Kaleidoscope, it would be found utterly
incapable of producing any of the fine forms which are peculiar to that
instrument.
If it were necessary to prove that Kircher and his pupils were entirely
ignorant of the positions of the eye and the object which are necessary
to the production of a picture, symmetrical in all its parts, and
uniformly illuminated, and that they went no farther than the mere
multiplication of forms that were previously regular and symmetrical,
we would refer the reader to Schottus’ _Magia Universalis Naturæ et
Artis_, printed at Wurtzbourg in 1657, where he repeats, almost word
for word, the description of Kircher, and adds the following curious
observation:—“But it is not only the objects placed in the semicircle
in the angle of the glasses that are seen and _multiplied_, but also
those which are more distant; for example, a wall, with its windows,
and in this case the multiplication produced by the mirrors will create
an immense public place, adorned with edifices and palaces.” This
passage shows, in the clearest manner, not only that the multiplication
of an object, independent of the union of the multiplied objects into
a symmetrical whole, was all that Kircher and his followers proposed
to accomplish; but also that they were entirely unacquainted with
the effects produced by varying the distance of the object from the
mirrors. If any person should doubt the accuracy of this observation,
we would request him to take Kircher’s two mirrors, to direct them to
a “wall with its windows,” either by Kircher’s method, or even by any
other way that he chooses, and to contemplate “the public place adorned
with edifices and with palaces.” He will see heaps of windows and of
walls, some of the heaps being much larger than others; and some being
farther from, and others nearer to, the centre; and some being dark,
and others luminous; while all of them are disunited. Let him now take
a Telescopic Kaleidoscope, and direct it to the same object; he will
instantly perceive the most perfect order arise out of confusion, and
he will not scruple to acknowledge, that no two things in nature can
be more different than the effects which are produced by these two
combinations of mirrors.
[Illustration: FIG. 55.]
[Illustration: FIG. 56.]
We come now to consider the claims of Mr. Bradley, Professor of
Botany in the University of Cambridge. In a work, entitled, _New
Improvements in Planting and Gardening_, published in 1717, this
author has drawn and described Kircher’s apparatus as an invention of
his own; and, instead of having in any respect improved it, he has
actually deteriorated it, in so far as he has made the breadth of the
mirrors greater than their height. An exact copy of the mirrors used
by Bradley is shown in Fig. 55, from which it will be at once seen,
that it is precisely the same as Kircher’s, shown in Fig. 54. We are
far from saying that Bradley stole the invention from Kircher, or that
Kircher stole it from Baptista Porta, or that Baptista Porta stole it
from the ancients. There is reason, on the contrary, to think that the
apparatus had been entirely forgotten, in the long intervals which
elapsed between these different authors, and there can be no doubt that
each of them added some little improvement to the instrument of their
predecessors. Baptista Porta saw the superiority of two mirrors, as a
multiplying machine, to a greater number used by the ancients. Kircher
showed the relation between the number of images and the inclination
of the mirrors; and Bradley, though he rather injured the apparatus,
yet he had the merit of noticing, that figures upon paper, which had a
certain degree of irregularity, like those in Fig. 56, could still form
a regular figure.
In order that the reader may fully understand Bradley’s method of using
the mirrors, we shall give it in his own words:—
“We must choose two pieces of looking-glass (says he), of equal
bigness, of the figure of a long square, _five_ inches in length, and
_four_ in breadth; they must be covered on the back with paper or silk,
to prevent rubbing off the silver, which would else be too apt to crack
off by frequent use. This covering for the back of the glasses must be
so put on, that nothing of it may appear about the edges on the bright
side.
“The glasses being thus prepared, they must be laid face to face, and
hinged together, so that they may be made to open and shut at pleasure,
like the leaves of a book; and now the glasses being thus fitted for
our purpose, I shall proceed to _explain the use of them_.
“Draw a large circle upon paper; divide it into three, four, five, six,
seven, or eight equal parts; which being done, we may draw in every one
of the divisions a figure, at our pleasure, either for garden-plats or
fortifications; as, for example, in Fig. 55, we see a circle divided
into six parts, and upon the division marked =F= is drawn part of a
design for a garden. Now, to see that design entire, which is yet
confused, we must place our glasses upon the paper, and open them to
the sixth part of the circle, _i.e._, one of them must stand upon the
line _b_, to the centre, and the other must be opened exactly to the
point _c_; so shall we discover an entire garden-plot in a circular
form (if we look into the glasses), divided into six parts, with as
many walks leading to the centre, where we shall find a basin of an
hexagonal figure.
“The line =A=, where the glasses join, stands immediately over the
centre of the circle, the glass =B= stands upon the line drawn from the
centre to the point =C=, and the glass =D= stands upon the line leading
from the centre to the point =E=: the glasses being thus placed, cannot
fail to produce the complete figure we look for; and so whatever equal
part of a circle you mark out, let the line =A= stand always upon the
centre, and open your glasses to the division you have made with your
compasses. If, instead of a circle, you would have the figure of a
hexagon, draw a straight line with a pen from the point _c_ to the
point _b_, and, by placing the glasses as before, you will have the
figure desired.
“So likewise a pentagon may be perfectly represented, by finding the
fifth part of a circle, and placing the glasses upon the outlines of
it; and the fourth part of a circle will likewise produce a square, by
means of the glasses, or, by the same rule, will give us any figure
of equal sides. I easily suppose that a curious person, by a little
practice with these glasses, may make many improvements with them,
which, perhaps, I may not have yet discovered, or have, for brevity
sake, omitted to describe.
“It next follows that I explain how, by these glasses, we may, from the
figure of a circle, drawn upon paper, make an oval; and also, by the
same rule, represent a long square from a perfect square. To do this,
open the glasses, and fix them to an exact square; place them over a
circle, and move them to and fro till you see the representation of
the oval figure you like best; and so, having the glasses fixed, in
like manner move them over a square piece of work till you find the
figure you desire of a long square. In these trials you will meet with
many varieties of designs. As for instance, Fig. 56, although it seems
to contain but a confused representation, may be varied into above
two hundred different representations, by moving the glasses over it,
which are opened and fixed to an exact square. In a word, from the most
trifling designs, we may, by this means, produce some thousands of good
draughts.
“But that Fig. 56 may yet be more intelligible and useful, I have drawn
on every side of it a scale, divided into equal parts, by which means
we may ascertain the just proportion of any design we shall meet within
it.
“I have also marked every side of it with a letter, as =A=, =B=, =C=,
=D=, the better to inform my reader of the use of the invention, and
put him in the way to find out every design contained in that figure.
“Example I.—Turn the side =A= to any certain point, either to the
north, or to the window of your room; and when you have opened your
glasses to an exact square, set one of them on the line of the side
=D=, and the other on the line of the side =C=, you will then have a
square figure four times as big as the engraved design in the plate:
but if that representation should not be agreeable, move the glasses
(still open to a square) to the number 5 of the side =D=, so will one
of them be parallel to =D=, and the other stand upon the line of the
side =C=, your first design will then be varied; and so by moving your
glasses, in like manner, from point to point, the draughts will differ
by every variation of the glasses, till you have discovered at least
fifty plans, differing from one another.
“Example II.—Turn the side marked =B=, of Fig. 56, to the same point
where =A= was before, and by moving your glasses as you did in the
former example, you will discover as great a variety of designs as
had been observed in the foregoing experiment; then turn the side
=C= to the place of =B=, and, managing the glasses in the manner I
have directed in the first example, you may have a great variety of
different plans, which were not in the former trials; and the fourth
side, =D=, must be managed in the same manner with the others; so that
from one plan alone, not exceeding the bigness of a man’s hand, we
may vary the figure at least two hundred times; and so, consequently,
from _five_ figures of the like nature, we might show about a thousand
several sorts of garden-plats; and if it should happen that the reader
has any number of plans for parterres or wilderness-works by him, he
may, by this method, alter them at his pleasure, and produce such
innumerable varieties, that it is not possible the most able designer
could ever have contrived.”
In reading the preceding description, the following conclusions cannot
fail to be drawn by every person who understands it.
1. Dr. Bradley, like Kircher, considers his mirrors as applicable to
regular figures, such as are represented in Fig. 55, and was entirely
unacquainted with the fact, that the inclination of the mirrors must
be an _even_ aliquot part of a circle. This is obvious, from his
stating that the mirrors may be set at the _third_, fourth, _fifth_,
sixth, _seventh_, or eighth part of a circle; for if he had tried to
set an irregular object between the mirrors when placed at the _third_,
_fifth_, or _seventh_ part of 360°, he would have found that a complete
figure could not possibly be produced.
2. From the erroneous position of the eye in front of the mirrors,
there is such an inequality of light in the reflected sectors, that the
last is scarcely visible, and therefore cannot be united into a uniform
picture with the real objects.
3. As the place of the eye in Bradley’s instrument is in front, and
therefore much nearer the object, or sector, seen by direct vision,
the angular magnitudes of all the different sectors are different,
and hence they cannot unite into a symmetrical figure. This is so
unavoidable a result of the erroneous position of the eye—a position
too, rendered necessary from the absurd form of the mirrors—that
Bradley actually employs his mirrors to convert a circle into an
ellipse, and a square into a rectangle!
4. In Bradley’s instrument, the sectors thus unequally shaped, and
unequally illuminated, are all separated from one another, by a space
equal to the thickness of the glass plates; and from the same cause,
the images reflected from the first surface interfere with those
reflected from the second, and produce a confusion or overlapping of
images entirely incompatible with a symmetrical picture.
These results are deduced upon the supposition that the object
consists of lines drawn upon the surface of paper, the only purpose
to which Bradley ever applied his mirrors; but when we attempt to use
these mirrors as a Kaleidoscope, and apply them to the objects which
are usually adapted to that instrument, we shall fail entirely, as
the mirrors are utterly incapable of producing the beautiful and
symmetrical forms which belong to that instrument.
We come now to consider the method of applying the mirrors to the
object shown in Fig. 55, which is an exact, but reduced copy of
Bradley’s figure. Because the angles of this figure are 90°, he directs
that the mirrors “be opened and fixed to an exact square; and that the
edge of one of the mirrors must always be placed so as to coincide
exactly with one of the sides of the rectangle, and carefully kept
in this line when the position of the mirrors is changed.” Hence it
is manifest, that Bradley was entirely ignorant of the fundamental
principle of the Kaleidoscope, namely, that if the inclination of the
mirrors is an even aliquot part of a circle, and if they are _set in
any position upon any object or set of objects, however confused,
or distorted, or irregular, they will create the most perfect and
symmetrical designs_. But even if Bradley had been aware of this
principle in theory, neither he nor any other person was acquainted
with the mode of constructing and fitting up the reflectors, in order
to render them capable of producing the effect. The position of the
eye, for symmetry of light, and for symmetry of form;—the position of
the mirrors, to produce a perfect junction of the last sectors;—the
position of the object necessary to produce an equality and perfect
junction between the object and the reflected images;—and the method
of accomplishing this for objects at all distances, were fundamental
points, in the combination of plane mirrors, which, so far as I
know, have never been investigated by any author. But even though a
knowledge of these theoretical points had been obtained, numerous
difficulties in the practical construction of the instrument remained
to be surmounted; and it required no slight degree of labour and
attention to enable the instrument to develop, in the most simple and
efficacious manner, the various effects which, in theory, it was found
susceptible of producing.
As the combination of mirrors, described by Kircher and Bradley, had
been long known to opticians, and had excited so little attention that
they had even ceased to be noticed in works on optical instruments, it
became necessary to discover some other origin for the Kaleidoscope.
The thirteenth and fourteenth Propositions of Wood’s _Optics_, and
some analogous propositions in Harris’s _Optics_, were therefore
presumed to be an anticipation of the invention. Professor Wood gives a
mathematical investigation of the number and arrangement of the images
formed by two reflectors, either inclined or parallel to each other.
These theorems assign no position to the eye, or to the object, and do
not include the principle of inversion, which is absolutely necessary
to the production of symmetrical forms. The theorems, indeed, which
have no connexion whatever with any instrument, are true, whatever
be the position of the eye or the object; and Mr. Wood has frankly
acknowledged, “that the effects produced by the Kaleidoscope were never
in his contemplation.”[22]
[22] See Appendix, p. 185.
The propositions in Harris’s _Optics_ relate, like Professor Wood’s,
merely to the multiplication and circular arrangement of the apertures
or sectors formed by the inclined mirrors, and to the progress of a
ray of light reflected between two inclined or parallel mirrors; and
no allusion whatever is made, in the propositions themselves, to any
instrument. In the propositions respecting the multiplication of the
sectors, the eye of the observer is never once mentioned; and the
proposition is true, if the eye has an infinite number of positions;
whereas, in the Kaleidoscope, the eye can only have one position. In
the other proposition (Prop. XVII.) respecting the progress of the
rays, the eye and the object are actually stated to be placed _between
the reflectors_; and even if the eye had been placed without the
reflectors, as in the Kaleidoscope, the position assigned it, at a
great distance from the angular point, is a demonstration that Harris
was _entirely ignorant of the positions of symmetry, either for the
object or the eye_, and could not have combined two reflectors so as to
form a Kaleidoscope for producing beautiful or symmetrical forms.[23]
It is important also to remark, that all Harris’s propositions relate
either to sectors or to small circular objects; and that he supposes
the very same effects to be produced when the inclination of the
mirrors is an _odd_, as when it is an _even_, aliquot part of a
circle. It is clear, therefore, that he was neither acquainted with
the fundamental point in the theory of the Kaleidoscope, nor with
any of its practical effects. The _only practical part_ of Harris’s
propositions is the fifth and sixth scholia to Prop. XVII. In the
fifth scholium he proposes a sort of catoptric box, or cistula,
known long before his time, composed of four mirrors, arranged in
a most unscientific manner, and containing opaque objects _between
the speculums_. “Whatever they are,” says he, when speaking of the
objects, “the upright figures between the speculums should be slender,
and not too many in number, otherwise they will too much _obstruct the
reflected rays from coming to the eye_.” This shows, in a most decisive
manner, that Harris knew nothing of the Kaleidoscope, and that he has
not even improved the common catoptric cistula, which had been known
long before. The principle of inversion, and the positions of symmetry,
were entirely unknown to him. In the sixth scholium, he speaks of rooms
lined with looking-glasses, and of luminous amphitheatres, which were
known even to the ancients, and have been described and figured by all
the old writers on optics.
[23] See Chap. I. pp. 11, 12, where we have shown that Harris was not
even acquainted with the way in which the last sector is formed by
reflexion.
APPENDIX.
Although I have no doubt that the observations contained in the
preceding Chapters are sufficient to satisfy every candid and
intelligent person respecting the true nature of all the combinations
of plane mirrors that preceded the invention of the Kaleidoscope, yet
as there are many who are incapable, from want of optical knowledge,
to understand the comparison which has been made between them, I shall
here present the opinions of four of the most eminent mathematicians
and natural philosophers.
The first of these is contained in a note from the late Professor
Wood, Master of St. John’s College, Cambridge, written in reply to a
letter, in which I requested him to say, if he had any idea of the
effects of the Kaleidoscope when he wrote the thirteenth and fourteenth
Propositions of his works on Optics.
“ST. JOHN’S, _May 19, 1818_.
“SIR,—The propositions I have given relating to the
number of images formed by plane reflectors, inclined to
each other, contain merely the mathematical calculation of
their number and arrangement. _The effects produced by
the Kaleidoscope were never in my contemplation._ My
attention has for some years been turned to other subjects,
and I regret that I have not time to read your Optical
Treatise, which I am sure would give me great pleasure.—I
am, Sir, your obedient humble servant,
“J. WOOD.”
The following is the opinion of the late celebrated Mr. James Watt:—
“It has been said here,” says Mr. Watt, “that you
took the idea of the Kaleidoscope from an old book on
gardening. My friend, the Rev. Mr. Corrie, has procured
me a sight of the book. It is Bradley’s Improvements of
Planting and Gardening. London, 1731, Part II. Chap. I.
It consists of two pieces of looking-glass, of equal bigness,
of the figure of a long square, five inches long, and four
inches high, hinged together upon one of the narrow sides,
so as to open and shut like the leaves of a book, which,
being set upon their edges upon a drawing, will show it
multiplied by repeated reflexions. This instrument I have
seen in my father’s possession seventy years ago, and frequently
since, but what has become of it I know not. In
my opinion, the application of the principle is very different
from that of your Kaleidoscope.”
The following is the opinion of the late Mr. Playfair, Professor of
Natural Philosophy in the University of Edinburgh:—
“EDINBURGH, _May 11, 1818_.
“I have examined the Kaleidoscope invented by Dr.
Brewster, and compared it with the description of an
instrument which it has been said to resemble, constructed
by Bradley in 1717. I have also compared its effect with
an experiment to which it may be thought to have some
analogy, described by Mr. Wood in his _Optics_, Prop. XIII.
and XIV.
“From both these contrivances, and from every optical
instrument with which I am acquainted, the Kaleidoscope
appears to differ essentially, both in its effect and in the
principles of its construction.
“As to the effect, the thing produced by the Kaleidoscope
is a series of figures presented with the most perfect
symmetry, so as always to compose a whole, in which
nothing is wanting and nothing redundant. It matters not
what the object be to which the instrument is directed; if
it only be in its proper place, the effect just described is
sure to take place, and with an endless variety. In this
respect the Kaleidoscope appears to be quite singular among
optical instruments. Neither the instrument of Bradley,
nor the experiment or theorem in Wood’s book, have any
resemblance to this; they go no further than the multiplication
of the figure.
“Next, as to the principle of construction, Dr. Brewster’s
instrument requires _a particular position of the eye of the
observer, and of the object looked at_, in order to produce its
effect. If either of these is wanting, the symmetry vanishes,
and the figures are irregular and disunited. In the other
two cases, no particular position, either for the eye or the
object, is required.
“For these reasons, Dr. Brewster’s invention seems to
me quite unlike the other two. Indeed, as far as I know,
it is quite singular among optical instruments; and it will
be matter of sincere regret, if any imaginary or vague analogy,
between it and other optical instruments, should be
the means of depriving the Doctor of any part of the reward
to which his skill, ingenuity, and perseverance, entitle him
so well.
“JOHN PLAYFAIR,
_Professor of Natural Philosophy in
the University of Edinburgh_.”
“_P.S._—Granting that there were a resemblance between
the Kaleidoscope and Bradley’s instrument, in any of the
particulars mentioned above, the introduction of coloured
and movable objects, at the end of the reflectors, is quite
peculiar to Dr. Brewster’s instrument. Besides this, a circumstance
highly deserving of attention, is the use of two
lenses and a draw-tube; so that the action of the Kaleidoscope
is extended to objects of all sizes, and at all distances
from the observer, and united, by that means, to the
advantages of the telescope.
“J. P.”
Professor Pictet’s opinion is stated in the following letter:—
“SIR,—Among your friends, I have not been one of the
least painfully affected by the shameful invasion of your
rights as an inventor, which I have been a witness of lately
in London. Not only none of the allegations of the invaders
of your patent, grounded on a pretended similarity
between your Kaleidoscope and Bradley’s instrument, or
such as Wood’s or Harris’s theories might have suggested,
appear to me to have any real foundation; but I can affirm,
that, neither in any of the French, German, or Italian
authors, who, to my knowledge, have treated of optics, nor
in Professor Charles’s justly-celebrated and most complete
collection of optical instruments at Paris, have I read or
seen anything resembling your ingenious apparatus, which,
from its numberless applications, and the pleasure it affords,
and will continue to afford to millions of beholders of its
matchless effects, may be ranked among the most happy
inventions that science ever presented to the lovers of
rational enjoyment.
“M. A. PICTET,
_Professor of Natural Philosophy in
the Academy of Geneva_.”
Those who wish to examine farther the ancient combinations of plane
mirrors, and other subjects connected with the Kaleidoscope, are
referred to the following works:—
Baptista Porta’s _Magia Naturalis_. Kircher’s _Ars Magna Lucis et
Umbræ_. Schottus’s _Magia Universalis Naturæ et Artis_. Bradley’s
_Treatise on Planting and Gardening_. Harris’s _Treatise on Optics_.
Wood’s _Optics_. Dr. Roget on the _Kaleidoscope_, in the _Annals
of Philosophy_, vol. xi. p. 375. _Encyclopædia Britannica_, Art.
KALEIDOSCOPE, _by_ Dr. Roget; and the _Compte Rendu des Travaux de
L’Académie de Dijon_, pour 1818, pp. 108-117.
Works by SIR DAVID BREWSTER.
MORE WORLDS THAN ONE: the Creed of the Philosopher, the
Hope of the Christian. Cr. 8vo., 4s. 6d.
THE MARTYRS OF SCIENCE: Galileo, Tycho Brahe, and
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THE KALEIDOSCOPE Practically Described. Cr. 8vo.,
_with Illustrations_, 4s. 6d.
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