118 



SCIENTIFIC RECREATIONS. 



illusion. We will continue our exposition as a means of finding an explana- 

 tion. In fig. 1 20, A and B present some examples pointed out by Hering ; 

 the straight, parallel lines, a b y 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 respect- 

 ively, 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 con- 

 vergence appears even more remarkable, whilst we notice less the apparent 

 deviation of the halves of the small lines, which are then horizontal and 



Fig. 1 20. The horizontal lines, a, b, c, d, are strictly parallel; their appearance of deviation is caused 



by the oblique lines. 



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 enlarge- 

 ment 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. 



In fig. 1 1 8 the narrow lines appear to turn towards the point where 

 they penetrate the thick line and disappear, to appear afterwards in continua- 

 tion 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 



