SPATIAL PERCEPTION. 



H43 



same lines, and his explanation is illustrated by Fig. 412, in which 

 n and n f represent vertical and oblique sections of the same eye, 

 looking at the point s in the triangle. Owing to the curvature factor, ab 



n' 



FIG. 412. Hering. 



will be relatively less under-estimated than cb, and the angle bca will 

 be seen too large as flea. If this explanation is correct, all triangles 

 will appear in different relations except one in which all three angles 

 are equal, namely, 60, and consequently this explana- 

 tion involves the under -estimation of angles under 60, 

 and the over-estimation of angles over 60, and, as 

 already mentioned, it is about this angle that the 

 illusion of Zollner's pattern ceases to be seen. 



The illusion of Fig. 408 has also been referred to the 

 influence of movement. It is supposed that the eye in 

 passing from b to c is interrupted, and the movement 

 taking place either with more difficulty or more slowly 

 than in passing from a to b gives rise to an appearance 

 of greater distance. Similarly, the fact that vertical 

 lines are over-estimated relatively to horizontal lines 

 has been referred to greater difficulty of vertical move- 

 ments. Unsatisfactory attempts have also been made 

 to refer the wrong estimation of angles and the various 

 related illusions to movement factors. 



. On the other hand, these illusions have been 

 referred exclusively to psychological factors. Lipps 1 

 has shown that the illusion that a square is longer 

 vertically than horizontally is greatly assisted by the 

 addition shown in Fig. 413, and he endeavours to explain this and all 

 the other illusions by supposing that they suggest certain mechanical 

 activities. 



Another illusion which has recently excited much discussion is that 



1 "Beitr. z. Psychol. u. Physiol. d. Siimesorg. , " Hamburg u. Leipzig, 1891, S. 219. 



FIG. 413. 



