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.