December 9, 1898.] 



SCIENCE. 



823 



have brought it into relation with the Z611- 

 ner patterns and have made use of it to 

 show that some other principle than the 

 overestimation of acute angles must be 

 emploj'ed in explaining the latter, since in 

 the new variant no acute angles are present. 



diagram until the angle between the line of 

 vision and the verticals equals about 30°. 

 In this position the lines of rectangles that 

 run away from the observer seem to form 

 each a series of low steps. Running the 

 eye along any vertical reveals this very 



Filelhne* has even attempted a perspective clearly. The reason is evident. The back- 



interpretation, according to which an ele- 

 ment of the illusion, held horizontallj^, rep- 

 resents a bench, one end of which recedes 

 into the background. As to the latter ex- 

 planation, not only does it involve the ar- 

 bitrary procedure of drawing additional 

 lines to represent the seat of the bench, or 

 of making the squares gradually smaller in 

 order to suggest the greater distance of one 

 end ; but, more than all, it can give no 

 satisfactory account of the illusion when 

 the line of squares, or rectangles, lies ver- 

 tically. There is, to be sure, a secondary 

 illusion in the figure, to which several ob- 

 servers have called attention, which might 

 lead one to suspect the presence of perspec- 

 tive elements. Hold Fig. 8 so that the 

 plane of the paper makes a small angle 

 with the line of vision. Then turn the 

 * Loe. cit , p. 42. 



ground, as it were, for any rectangle viewed 

 in this way is partly a white area, partly a 

 similar black area. These areas are so dis- 

 tributed that when dark area is followed by 

 dark area the middle portion of these joined 

 areas must seem somewhat darker than the 

 outlying parts, since the latter have received 

 a grayish tinge from the white areas beyond. 

 This darker portion can be interpreted only 

 as a part Ij'ing in shadow, and hence the il- 

 lusory perception of a low step, the ' riser' 

 being the shadowed portion. 



But as surely as this secondary illusion 

 rests upon one of the accessory criteria of 

 perspective vision, just as little can it 

 furnish anj' basis for the perspective ex- 

 planation of the primary illusion. That this 

 is due to irradiation cannot now be doubted. 

 The present writer endeavored recently* to 



* I'syclwlogical Review, V. (1898), 233 



