OPTICAL ILLUSIONS—ZOLLNER’S DESIGNS—THE
THAUMATROPE—PHENOKISTOSCOPE—THE ZOOTROPE—THE PRAXINOSCOPE—THE DAZZLING
TOP.
We shall now continue the subject by describing some illusions more
curious still—those of _ocular estimation_. These illusions depend
rather on the particular properties of the figures we examine, and the
greater part of these phenomena may be placed in that category whose
law we have just formulated: _the differences clearly perceived appear
greater than the differences equal to them, but perceived with greater
difficulty_. Thus a line —— when divided appears greater than when not
divided; the direct perception of the parts makes us notice the number
of the sub-divisions, the size of which is more perceptible than when
the parts are not clearly marked off. Thus, in fig. 115, we imagine the
length _ab_ equals _bc_, although _ab_ is in reality longer than _bc_.
In an experiment consisting of dividing a line into two equal parts,
the right eye tends to increase the half on the right, and the left eye
to enlarge that on the left. To arrive at an exact estimate, we turn
over the paper and find the exact centre.
[Illustration: Fig. 115.]
[Illustration: Fig. 116.]
Illusions of this kind become more striking when the distances to be
compared run in different directions. If we look at A and B (fig. 116),
which are perfect squares, A appears greater in length than width,
whilst B, on the contrary, appears to have greater width than length.
The case is the same with angles. On looking at fig. 117, angles 1,
2, 3, 4 are straight, and should appear so when examined. But 1 and 2
appear pointed, and 3 and 4 obtuse. The illusion is still greater if we
look at the figure with the right eye. If, on the contrary, we turn it,
so that 2 and 3 are at the bottom, 1 and 2 will appear greatly pointed
to the left eye. The divided angles always appear relatively greater
than they would appear without divisions.
The same illusion is presented in a number of examples in the course of
daily life. An empty room appears smaller than a furnished room, and a
wall covered with paperhangings appears larger than a bare wall. It is
a well-known source of amusement to present someone in company with a
hat, and request him to mark on the wall its supposed height from the
ground. The height generally indicated will be a size and a half too
large.
We will relate an experience described by Bravais: “When at sea,”
he says, “at a certain distance from a coast which presents many
inequalities, if we attempt to draw the coastline as it presents
itself to the eye, we shall find on verification that the horizontal
dimensions have been correctly sketched at a certain scale, while all
the vertical angular objects have been represented on a scale twice as
large. This illusion, which is sure to occur in estimates of this kind,
can be demonstrated by numerous observations.”
M. Helmholtz has also indicated several optical illusions.
[Illustration: Fig. 117.]
[Illustration: Fig. 118.]
[Illustration: Fig. 119.]
If we examine fig. 118, the continuation of the line _a_ does not
appear to be _d_,—which it is in reality,—but _f_, which is a little
lower. This illusion is still more striking when we make the figure on
a smaller scale (fig. 119), as at B, where the two fine lines are in
continuation with each other, but do not appear to be so, and at C,
where they appear so, but are not in reality. If we draw the figures
as at A (fig. 118), leaving out the line _d_, and look at them from
a gradually increasing distance, so that they appear to diminish, it
will be found that the further off the figure is placed, the more it
seems necessary to lower the line _f_ to make it appear a continuation
of _a_. These effects are produced by irradiation; they can also be
produced by black lines on a white foundation. Near the point of the
two acute angles, the circles of diffusion of the two black lines touch
and mutually reinforce each other; consequently the retinal image of
the narrow line presents its maximum of darkness nearest to the broad
line, and appears to deviate on that side. In figures of this kind,
however, executed on a larger scale, as in fig. 118, irradiation
can scarcely be the only cause of illusion. We will continue our
exposition as a means of finding an explanation. In fig. 120, A and B
present some examples pointed out by Hering; the straight, parallel
lines, _a b_, and _c d_, appear to bend outwards at A, and inwards
at B. But the most striking example is that represented by fig. 121,
published by Zollner.
The vertical black strips of this figure are parallel with each other,
but they appear convergent and divergent, and seem constantly turned
out of a vertical position into a direction inverse to that of the
oblique lines which divide them. The separate halves of the oblique
lines are displaced respectively, like the narrow lines in fig. 119.
If the figure is turned so that the broad vertical lines present
an inclination of 45° to the horizon, the convergence appears even
more remarkable, whilst we notice less the apparent deviation of the
halves of the small lines, which are then horizontal and vertical. The
direction of the vertical and horizontal lines is less modified than
that of the oblique lines. We may look upon these latter illusions as
fresh examples of the aforesaid rule, according to which acute angles
clearly defined, but of small size, appear, as a rule, relatively
larger when we compare with obtuse or right angles which are undivided;
but if the apparent enlargement of an acute angle shows itself in such
a manner that the two sides appear to diverge, the illusions given in
figs. 118, 120, and 121, will be the result.
[Illustration: Fig. 120.—The horizontal lines, _a_, _b_, _c_, _d_,
are strictly parallel; their appearance of deviation is caused by the
oblique lines.]
In fig. 118 the narrow lines appear to turn towards the point where
they penetrate the thick line and disappear, to appear afterwards in
continuation of each other. In fig. 120 the two halves of each of the
two straight lines seem to deviate through the entire length in such
a manner that the acute angles which they form with the oblique lines
appear enlarged. The same effect is shown by the vertical lines of fig.
121.
M. Helmholtz is of opinion (figs. 120, 121) that the law of contrast
is insufficient to entirely explain the phenomena, and believes that
the effect is also caused by the movements of the eye. In fact, the
illusions almost entirely disappear, if we fix on a point of the object
in order to develop an accidental image, and when we have obtained one
very distinctly, which is quite possible with Zollner’s design (fig.
121), this image will present not the slightest trace of illusion. In
fig. 118 the displacement of the gaze will exercise no very decided
influence on the strengthening of the illusion; on the contrary, it
disappears when we turn our eyes on the narrow line, _ad_. On the other
hand, the fixing of the eyes causes the illusion to disappear with
relative facility in fig. 120, and with more difficulty in fig. 121;
it will, however, disappear equally in the latter design, if we fix it
immovably, and instead of considering it as composed of black lines on
a white background, we compel ourselves to picture it as white lines on
a black foundation; then the illusion vanishes. But if we let our eyes
wander over the illustration, the illusion will return in full force.
We can indeed succeed in completely destroying the illusion produced by
these designs by covering them with a sheet of opaque paper, on which
we rest the point of a pin. Looking fixedly at the point, we suddenly
draw away the paper, and can then judge if the gaze has been fixed and
steady according to the clearness of the accidental image which is
formed as a result of the experiment.
[Illustration: Fig. 121.—The vertical strips are parallel; they appear
convergent or divergent under the influence of the oblique lines.]
[Illustration: Fig. 122.—Observation of electric spark.]
The light of an electric spark furnishes the surest and simplest means
of counteracting the influence of movements of the eyes, as during the
momentary duration of the spark the eye cannot execute any sensible
movement. For this experiment the present writer has made use of a
wooden box, A B C D (fig. 122), blackened on the inside. Two
holes are made for the eyes on each side of the box, _f_ and _g_. The
observer looks through the openings, _f_, and in front of openings,
_g_, the objects are placed; these are pierced through with a pin,
which can be fixed by the eyes in the absence of the electric spark,
when the box is perfectly dark. The box is open, and rests on the
table, B D, to allow of changing the object. The conducting
wires of electricity are at _h_ and _i_; in the centre of the box is a
strip of cardboard, white on the side facing the spark, the light of
which it shelters from the eye of the observer and throws back again
on the object. With the electric light the illusion was completely
perceptible with fig. 118, while it disappeared altogether in fig. 120;
with fig. 121 it was not entirely absent, but when it showed itself,
it was much more feeble and doubtful than usual, though the intensity
of light was quite sufficient to allow of the form of the object being
very distinctly examined. Thus two different phenomena have to be
explained; first, the feeble illusion which is produced without the
intervention of movements of the eye; and secondly, the strengthening
of the illusion in consequence of these movements. The law of contrast
sufficiently explains the first; that which one perceives most
distinctly with indirect vision is the concordance of directions with
dimensions of the same kind. We perceive more distinctly the difference
of direction presented at their intersection by the two sides of an
acute or obtuse angle, than the deviation that exists between one of
the sides and the perpendicular which we imagine placed on the other
side, but which is not marked. By being distributed on both sides,
the apparent enlargement of the angles gives way to displacements,
and changes of direction of the sides. It is difficult to correct
the apparent displacement of the lines when they remain parallel to
their true direction; for this reason, the illusion of the figure is
relatively more inflexible. Changes of direction, on the contrary,
are recognised more easily if we examine the figure attentively, when
these changes have the effect of causing the concordance of the lines
(which accord in reality) to disappear; it is probably because of the
difference in aspect of the numerous oblique lines of figs. 120 and
121 that the concordance of these lines escapes the observer’s notice.
As regards the influence exercised by the motion of the eyes in the
apparent direction of the lines, M. Helmholtz, after discussing the
matter very thoroughly, proves the strengthening of the illusion in
Zollner’s illustration to be caused by those motions. It is not now our
intention to follow out the whole of this demonstration; it will be
sufficient to point out to the reader a fruitful force of study, with
but little known results.
The Romans were well acquainted with the influence of oblique lines. At
Pompeii, fresco paintings are to be found, in which the lines are not
parallel, so that they satisfy the eye influenced by adjacent lines.
Engravers in copper-plate have also studied the influence of _etchings_
on the parallelism of straight lines, and they calculate the effect
that they will produce on the engraving. In some ornamentations in
which these results have not been calculated, it sometimes happens that
parallel lines do not appear parallel because of the influence of other
oblique lines, and a disagreeable effect is produced. A similar result
is to be seen at the railway station at Lyons, the roof of which is
covered with inlaid work in _point de Hongrie_. The wide parallel lines
of this ceiling appear to deviate, a result produced by a series of
oblique lines formed by the planks of wood.
[Illustration: Fig. 123.—Two sides of a Thaumatrope disc.]
Having given a long account of the result of M. Helmholtz’s labours,
we will pass to the consideration of another kind of experiments,
or rather appliances, based on the illusions of vision, and the
persistence of impressions on the retina.
The Thaumatrope, to which we have already referred, is a plaything
of very ancient origin, based on the principle we have mentioned. It
consists of a cardboard disc, which we put in motion by pulling two
cords. On one side of the disc a cage, _a_, is portrayed, on the other
a bird, _b_ (fig. 123). When the little contrivance is turned round,
the two designs are seen at the same time, and form but one image—that
of a bird in its cage (fig. 124). It is of course hardly necessary to
add that the designs may be varied.
We have already referred to M. Plateau’s rotating disc (the
Phenakistoscope). Through the narrow slits we perceive in succession
representations of different positions of a certain action. The
persistence of the luminous impressions on the retina gives to the eye
the sensation of a continuous image, which seems animated by the same
movements as those portrayed in the different phases (fig. 125).
[Illustration: Fig. 124.—Appearance of the Thaumatrope in rotation.]
[Illustration: Fig. 125.—Plateau’s Phenokistoscope.]
The Zootrope (fig. 126) is a perfected specimen of this apparatus. It
is composed of a cylinder of cardboard, turning on a central axis.
The cylinder is pierced with vertical slits at regular intervals, and
through which the spectator can see the designs upon a band of paper
adapted to the interior of the apparatus in rotation. The designs are
so executed that they represent the different times of a movement
between two extremes; and in consequence of the impressions upon the
retina the successive phases are mingled, so the spectator believes he
sees, without transition, the entire movement. We give a few specimens
of the pictures for the Zootrope (fig. 127). We have here an ape
leaping over a hedge, a dancing “Punch,” a gendarme pursuing a thief,
a person holding the devil by the tail, a robber coming out of a box,
and a sportsman firing at a bird. The extremes of the movement are
right and left; the intermediary figures make the transitions, and they
are usually equal in number to the slits in the Zootrope. It is not
difficult to construct such an instrument, and better drawings could be
made than the specimens taken at random from a model. The earth might
be represented turning in space, or a fire-engine pumping water could
be given, and thus the Zootrope might be quite a vehicle of instruction
as well as of amusement. This instrument is certainly one of the most
curious in the range of optics, and never fails to excite interest. The
ingenious contrivances which have up to the present time reproduced it,
all consist in the employment of narrow slits, which besides reducing
the light to a great extent, and consequently the light and clearness
of the object, require the instrument to be set in rapid rotation,
which greatly exaggerates the rapidity of the movements represented,
and without which the intermissions of the spectacle could not unite in
a continuous sensation.
[Illustration: Fig. 126.—The Zootrope.]
[Illustration: Fig. 127.—Pictures used in the Zootrope.]
We present here an apparatus based on a very different optical
arrangement. In the _Praxinoscope_[12] (a name given by the inventor,
Mr. Reynaud, to this new apparatus), the substitution of one object for
another is accomplished without interruption in the vision, or solution
of continuity, and consequently without a sensible reduction of light;
in a word, the eye beholds _continuously_ an image which, nevertheless,
is incessantly changing before it. The result was obtained in this
manner. Having sought unsuccessfully by mechanical means to substitute
one object for another without interrupting the continuity of the
spectacle, the inventor was seized with the idea of producing this
substitution, not with the objects themselves, but with their virtual
images. He then contrived the arrangement which we will now describe.
A plane mirror, AB (fig. 129), is placed at a certain distance from
an object, CD, and the virtual image will be seen at C′D′. If we then
turn the plane mirror and object towards the point, O, letting BE and
DF be their new positions, the image will be at C″D″. _Its axis_, O,
_will not be displaced_. In the positions, AB and CD, first occupied
by the plane mirror and the object, we now place another mirror and
object. Let us imagine the eye placed at M. Half of the first object
will be seen at OD″, and half of the second at OC′. If we continue
the rotation of the instrument, we shall soon have mirror No. 2 at
TT′, and object No. 2 at SS′. At the same moment the image of object
No. 2 will be seen entirely at C‴D″. Mirror No. 2 and its object will
soon after be at BE and DF. If we then imagine another mirror and its
corresponding object at AB and CD, the same succession of phenomena
will be reproduced. This experiment therefore shows that a series of
objects placed on the perimeter of a polygon will be seen successively
at the centre, if the plane mirrors are placed on a concentric polygon,
the “apothème” of which will be less by one-half, and which will be
carried on by the same movement. In its practical form, M. Reynaud’s
apparatus consists of a polygonal or simply circular box (fig. 128),
(for the polygon may be replaced by a circle without the principle or
result being changed), in the centre of which is placed a prism of
exactly half a diameter less, the surface of which is covered with
plane mirrors. A strip of cardboard bearing a number of designs of
the same object, portrayed in different phases of action, is placed
in the interior of the circular rim of the box, so that each position
corresponds to a plate of the glass prism. A moderate movement of
rotation given to the apparatus, which is raised on a central pivot,
suffices to produce the substitution of the figures, and the animated
object is reflected on the centre of the glass prism with remarkable
brightness, clearness, and delicacy of movement. Constructed in this
manner, the _Praxinoscope_ forms an optical toy both interesting and
amusing. In the evening, a lamp placed on a support _ad hoc_, in the
centre of the apparatus, suffices to light it up very clearly, and a
number of persons may conveniently assemble round it, and witness the
effects produced.
[Illustration: Fig. 128.—M. Reynaud’s Praxinoscope.]
[Illustration: Fig. 129.]
Besides the attractions offered by the animated scenes of the
_Praxinoscope_, the apparatus may also be made the object of useful
applications in the study of optics. It permits an object, a drawing,
or a colour, to be substituted instantaneously in experiments on
secondary or subjective images, etc., on the contrast of colours or
the persistence of impressions, etc. We can also make what is called
a _synthesis of movements_ by placing before the prism a series of
diagrams of natural objects by means of photography.
M. Reynaud has already arranged an apparatus which exhibits in the
largest dimensions the animated reflection of the _Praxinoscope_, and
which lends itself to the demonstration of curious effects before
a numerous auditory. The ingenious inventor has recently contrived
also a very curious improvement in the original apparatus. In the
_Praxinoscope Theatre_ he has succeeded in producing truly ornamental
_tableaux_, as on a small Lilliputian stage, in the centre of which the
principal object moves with startling effect. To obtain this result, M.
Reynaud commences by cutting out in black paper the different figures,
the whole of which will form an object animated by the rotation
given to the _Praxinoscope_. To supply the decorations, he arranges
on the black foundation the image of an appropriate coloured design
by means of a piece of glass. It is well known that transparent glass
possesses the property of giving a reflection of the objects on the
nearest side as well as on the farthest. We may recall the applications
of this optical effect in theatres, and also in courses of physics,
under the title of _impalpable spectres_. It is also by reflection
on thin, transparent glass, that M. Reynaud produces the image of
the ornamentations in the _Praxinoscope Theatre_. The decorations
are really placed in the lid, which is held by a hook in a vertical
position, thus forming the front side of the apparatus (fig. 130). In
this side a rectangular opening is made, through which the spectator
(using both eyes) perceives at the same time the animated reflection
of the _Praxinoscope_, and the immovable image of the decorations
reflected in the transparent glass. The position of the latter and
its distance from the coloured decorations are arranged so that the
reflection is thrown behind the moving figure, which consequently
appears in strong relief against the background, the effect produced
being very striking. It is evident that to change the decorations it
is only necessary to place in succession on a slide the different
_chromos_ representing landscapes, buildings, the interior of a
circus, etc. It is easy to choose an arrangement suitable for each of
the moving figures placed in the _Praxinoscope_. By this clever and
entirely novel optical combination, the mechanism of the contrivance
is entirely lost sight of, leaving only the effect produced by the
animated figures, which fulfil their different movements on the little
stage. The _Praxinoscope Theatre_ can also be used as well in the
evening as in the daytime. By daylight, it is sufficient to place it
before a window, and in the evening the same effects may be produced,
perhaps in even a more striking manner, by simply placing a lamp on the
stand, with a small plated reflector, and a lamp-shade. The illusion
produced by this scientific plaything is very complete and curious,
and M. Reynaud cannot be too much commended for so cleverly applying
his knowledge of physics in the construction of an apparatus which is
at the same time both an optical instrument and a charming source of
amusement.
[Illustration: Fig 130.—The Praxinoscope Theatre.]
[Illustration: Fig. 131.—The Dazzling Top.]
Amongst the toys founded upon the persistency of impressions upon the
retina we may instance the “Dazzling Top” (fig. 131). This remarkable
invention is quite worthy of a place in every cabinet, and is an
ingenious specimen of a perfected Helmholtz top. It is a metallic toy
put in motion by means of a cord wound round a groove. The axis is
hollow, admits a metallic stem, and fits into a handle which is held in
the hand. The top is placed upon a little cup in an upright position,
and it is then set spinning in the usual way with the cord. The stem
and handle are then withdrawn, and as the top will continue to spin for
a long time, discs and various outline shapes can be fixed upon it, and
various objects will be shadowed thereon. Cups, bowls, candlesticks,
and jugs can be seen plainly revolving as the top carries the wire
representation in outline rapidly past the eyes. Coloured cardboard can
be worked into various patterns, and much amusement will be created
amongst children and young people.
FOOTNOTES:
[12] From _praxis_, action, and _skopein_, to show.