ON THE CONSTRUCTION AND USE OF POLYANGULAR
KALEIDOSCOPES, IN WHICH THE REFLECTORS CAN BE FIXED
AT ANY ANGLE.
In all the preceding instruments, the reflecting planes are fixed at
an invariable angle, which is some even aliquot part of 360°; and
therefore, though the forms or patterns which they create are literally
infinite in number, yet they have all the same character, in so far
as they are composed of as many pairs of direct and inverted images
as half the number of times that the inclination of the reflectors is
contained in 360°.
It is therefore of the greatest importance, in the application of the
Kaleidoscope to the arts, to have it constructed in such a manner, that
patterns composed of any number of pairs of direct and inverted images
may be created and drawn. With this view, the instrument may be fitted
up in various ways, with paper, cloth, and metallic joints, by means
of which the angle can be varied at pleasure; but the most convenient
methods are shown in the Figures from Fig. 29 to 35, inclusive, which
represent two different kinds of Polyangular Kaleidoscopes, as made by
the late Mr. R. B. Bate, Optician, London, who had devoted much time
and attention to the perfection of this species of Kaleidoscope.
_Bate’s Polyangular Kaleidoscope with Metallic Reflectors._
[Illustration: FIG. 29.]
[Illustration: FIG. 30.]
The three Figures, viz., 29, 30, and 31, represent the Polyangular
Kaleidoscope with metallic reflectors, as made by Mr. Bate. Fig. 29
shows the complete instrument, when mounted upon a stand; Fig. 30
is a section of it in the direction of its length; Fig. 31 is a
transverse section of it through the line =S T=, Fig. 30, and Fig. 32
shows the lens of the eye-hole =E=. The tube of this instrument is
composed of two cones, =M M=, =N N=, Fig. 30, connected together by a
middle piece or ring, =R R=, into which they are both screwed. These
two cones enclose two highly polished metallic reflectors, =A O=, =B
O=, Fig. 31, only one of them, viz., =B O E=, being seen in Fig. 30.
One of these reflectors, =B O E=, is fixed to the ring =R R=, by the
intermediate piece =K G L=. The reflector is screwed to this piece by
the adjustable screws =K=, =L=; and the piece =K G L= is again fixed
to the ring =R R=, by two screws seen above and below =G=, in Fig. 31.
Hence the tube, consisting of the cones =M M=, =N N=, and the ring =R
R=, are immovably connected with the mirror =B O E=. The surface of the
reflector =B O E= is adjusted by the screws at =K= and =L=, till it
passes accurately through the axis of the cones and ring as seen in
Fig. 31. The other reflector =A O=, is fixed to an outer ring _r r_,
by means of an intermediate piece, similar to =K G L=, the arm =F= of
which, corresponding to =G=, passes through an annular space or open
arch, of more than 90°, cut out of the circumference of the inner ring
=R R=. The arm =F= is fixed to the outer ring _r r_ by two screws,
seen above and below =F=; and the reflector =A O= is fixed to the bar
corresponding to =K L=, Fig. 30, by similar screws, for the purpose of
adjusting it.
[Illustration: FIG. 31.]
[Illustration: FIG. 32.]
The lower edge =O E= of the reflector =B O E= extends about the 15th of
an inch below the axis of the cones, as represented by the dotted line
in Fig. 30; but the lower edge =O E= of the other reflector =A O E=,
which is finely ground to an acute angle, forming a perfectly straight
and smooth line, is placed exactly in the axis of the cones, so as just
to touch a line in the reflector =A O E=, which coincides with the axis
of the cone, and to form a junction with that line in every part of
the two meeting planes. The very nice adjustments which are necessary
to produce so exact a motion are effected by the screws corresponding
to =K= and =L=.
If we now fix the outer ring _r r_ into the ring of a stand =S T=,
so as to be held fast, and turn the cones with the hand, we shall
give motion to the reflector =B O=, so as to place it at any angle
we please, from 0° to 90°; and during its motion through this arch,
the junction of the two reflectors must remain perfect, if the
touching lines are adjusted, as we have described them, to the axis
of motion, which must also be the axis of the cones and rings. If, on
the contrary, we take away the stand, and, holding the instrument in
the hand by either of the cones =M=, =N=, turn the ring =R R= with
the other, we shall give motion to its reflector =A O=, and produce a
variation in the angle in the same manner as before. The same effect
may be produced by an endless screw working in teeth, cut upon the
circumference of the outer ring _r r_.
In order to enable the observer to set the reflectors at once to any
even aliquot part of a circle, or so as to give any number of pairs of
direct and inverted images, the most convenient of the even aliquot
parts of the circle are engraven upon the ring _r r_; so that we have
only to set the index to any of these parts, to the number 12, for
example, and the reflectors will then be placed at an angle of 30° (12
× 30 = 360°), and will form a circular field with _twelve_ luminous
sectors, or a star with _six_ points, and consequently a pattern
composed of _six_ pairs of direct and inverted images.
As the length of the plates is only about five inches, it is
necessary, excepting for persons very short-sighted, to have a convex
lens placed in front of the eye-hole =E=, as shown in Figs. 30 and
32. A brass ring containing a plane glass screws into the outer ring
=C D=, when the instrument is not in use; and there is an object-box
containing fragments of differently coloured glass. This object-box
consists of two plates of glass, one ground and the other transparent,
set in brass rims. The transparent one goes nearest the reflector, and
the brass rim which contains it screws into the other, so as to enclose
between them the coloured fragments, and regular figures of coloured
and twisted glass. A loose ring surrounds this object-box; and when
this ring is screwed into the circular rim =C D=, the object-box can be
turned round so as to produce a variety of patterns, without any risk
of its being detached from the outer cone.
In applying this instrument to opaque objects, such as engravings,
coins, gems, or fragments of coloured glass laid upon a mirror, the
aperture of the mirrors is laid directly over them, the large cone
=M M= having been previously unscrewed, for the purpose of allowing
the light to fall freely upon the objects. This property of the
Kaleidoscope is of great importance, as in every other form of the
instrument opaque objects must be held obliquely, and therefore at
such a distance from the reflectors as must affect the symmetry of the
pattern.
As the perfection of the figures depends on the reflectors being kept
completely free of dust, particularly at their junction, where it
naturally accumulates, the greatest facility is given by the preceding
construction in keeping them clean. For this purpose, the large cone
must be unscrewed; the reflectors having been previously closed, by
turning the index to 60 on the ring. They are next to be opened to
the utmost, and the dust may in general be removed by means of a fine
point wrapped in clean and dry wash-leather. If any dust, however,
still adheres, the small screw in the side of the ring opposite
to the index should be removed, and the smaller cone, =N N=, also
unscrewed. By easing the supporting screws of either of the reflectors,
their touching sides will separate, so as to allow a piece of dry
wash-leather to be drawn between them. When every particle of dust has
been thus removed, the metals should be re-adjusted and closed before
the cones are replaced; both of which should be screwed firmly into the
ring =R R=.
As the axis of motion in the preceding construction is necessarily the
axis of the cones and rings, the diameter of these cones and rings must
everywhere be double the breadth of the reflectors. From this cause,
the tube, and consequently the object-box, are wide, and the instrument
is, to a certain degree, not very portable. This defect is completely
avoided in another Polyangular Kaleidoscope constructed by Mr. Bate,
upon entirely different principles, which we shall now proceed to
describe.
_Bate’s Polyangular Kaleidoscope with Glass Reflectors._
[Illustration: FIG. 33.]
[Illustration: FIG. 34.]
[Illustration: FIG. 35.]
[Illustration: FIG. 36.]
A section of the whole of this instrument, in the direction of its
length, is shown in Fig. 33. A section through =M N= or =O P=, near
the eye-end, is shown in Fig. 35, Fig. 34 representing the mode of
supporting the fixed reflector, and Fig. 36 the mode of supporting
the movable reflector. The tube of the Kaleidoscope, in Fig. 33, is
represented by _b c d e f g h_, and consists of two parts, _b c g h_,
and _c d e f g_. The first of these parts unscrews from the second,
and the second contains all the apparatus for holding and moving the
reflectors. At the parts =M N O P=, of the tube, are inserted a short
tube, a section of which is shown in Fig. 34. The object of these tubes
is to support the fixed mirror =A O=, which rests with its lower end
=O= upon the piece of brass _t_. It is kept from falling forwards by
the tongue _r_, connected with the upper part _s s_, and from falling
backward by the piece of cork =Q=, which may be removed at any time,
for the purpose of taking out and cleaning the reflectors. This
little tube is fixed to the outer tube by the screws _s_, _s_. The
contrivance for supporting and moving the second reflector =B O=, is
shown in Fig. 36, in section; and a longitudinal view of it is given
in Fig. 33. The mirror =B O= lies in an opening, cut into two pieces
of brass, =_v_ B _p_=, one of which is placed at =M N=, and the other
at =O P=. These two pieces of brass are connected by a rod _m n_,
Fig. 33; and in the middle of this rod there is inserted a screw _k_,
which passes through the main tube _c d e f g_, into a broad milled
ring _w w_, which revolves upon the tube. As the screw _k_, therefore,
fastens the ring _w w_ to the rod _m n_, the reflector =B O= will be
supported in the tube by the ring _w w_. The lower part of the mirror
=B O=, or rather of the brass piece =_v_ B _p_=, rests at _y_, upon
the piece of watch-spring _x y z_, fastened to the main tube at _z_.
This spring presses the face of the reflector =B O= against the ground
and straight edge of the other reflector =A O=, so as always to effect
a perfect junction in every part of their length:—The apparatus for
both reflectors is shown in Fig. 35. An arch of about 45° is cut out
of the main tube, so as to permit the screw _k_ to move along it; and
hence, by turning the broad ring _w w_, the reflector =B O= may be
brought nearly to touch the reflector =A O=, and to be separated from
it by an arch of 45°, so as to form every possible angle from nearly
0° to 45°, which is a sufficient range for the Kaleidoscope. The main
tube terminates in a small tube at =E=, upon which may be screwed, when
it is required, a brass cap _e f_, containing a convex lens. A short
tube, or cell, _a a a a_, for containing the object-boxes, slips upon
the end of the tube, and should always be moved round from right to
left, in order that the motion may not unscrew the portion of the tube
_b c g h_, upon which it moves. When the instrument is used for opaque
objects, the end piece, _b c g h_ of the tube, screws off, so as to
admit the light freely upon the objects.
The advantages which the Polyangular Kaleidoscopes possess over all
others are—
1st, That patterns of any number of sectors, from the
simplest to the most complicated, can be easily
obtained.
2d, That the reflectors can be set, with the most
perfect accuracy, to an even aliquot part of a
circle.
3d, That the reflectors can be at any time completely
cleaned and freed from all the dust that
accumulates between them, and the instrument
rendered as perfect as when it came from the hands
of the maker.
In order to apply this Kaleidoscope to distant objects, or make it
telescopic,[6] a piece of tube with a lens at the end of it is put upon
the end piece, _b c g h_, and may be suited to different distances
within a certain range.
[6] See Chapter X.