820 



SCIENCE. 



[N. S. Vol. VIII. No. 206. 



some feet from it. The illusion persists, 

 and yet there is no possible attempt to give 

 an independent perspective interpretation 

 to either end of the rope. Still more con- 

 clusive, perhaps, is the consideration of the 

 so-called ' Illusion of the Gothic Arch,' a 

 representation of which is given in Fig. 4. 



This illusion, many times independently 

 observed, is manifestly but a variant of the 

 more simple rectangular form, and its strik- 

 ing quality is not destroyed even though 

 the observer be most intensely conscious 

 that he is in the presence of actual objects, 

 seen under the conditions of normal per- 

 spective. It seems most necessary, there- 

 fore, to look askance at this most recent 

 attempt to apply the perspective interpreta- 

 tion to the Foggendorff figure. 



One point seems to have been universally 

 overlooked in the quantitative investiga- 

 tions made upon this figure. All measure- 

 ments, namely, so far as one can judge 

 from the literature of the subject, have 

 proceeded upon the assumption that the 

 amount of the illusory displacement is to 

 be discovered by moving one end of the 

 transversal vertically along the strip, the 

 moving line to be kept always parallel to 

 itself, until the point is reached where the 



two parts seem continuous. It would seem, 

 however, that an unprejudiced approach 

 to the problem should lead one to make 

 room for any possible angular displacement 

 that might be required to bring the moving 

 end into a position of satisfactory apparent 

 continuation with the fixed end. The writer 

 recently constructed an apparatus which 

 allows the determination of both vertical 

 and rotatory displacement, but the meager 

 results thus far obtained give no basis for 

 any conclusion in the matter. Still the 

 point seems well worthy of more extended 

 attention. 



3. The Muller-Lyer Figure. — Figure 5 pre- 

 sents in its typical form the much- discussed 



-3 



' optical paradox,' first published by Miiller- 

 Lyer in 1889, in the Archiv fur Physiologie. 

 No less than eight diflTerent explanations for 

 this illusion have been propounded and 

 warmly defended by the various writers. 

 This number has been so far reduced by 

 the reciprocal overthrow of the contesting 

 parties that only three attempts at an expla- 

 nation need detain us here, (a) Theper«pec- 

 tive theory is less fortunate here than usual. 



