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