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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.

Fig. 115.

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.

Fig. 117.

Fig. 118.

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.

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.

Fig. 121.—The vertical strips are parallel; they appear convergent or divergent under the influence of the oblique lines.

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.

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).

Fig. 124.—Appearance of the Thaumatrope in rotation.

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.

Fig. 126.—The Zootrope.

Fig. 127.—Pictures used in the Zootrope.

We present here an apparatus based on a very different optical arrangement. In the Praxinoscope12 (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.

Fig. 128.—M. Reynaud’s Praxinoscope.

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.

Fig 130.—The Praxinoscope Theatre.

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.