826 



SCIENCE. 



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



sion that seems to throw some light upon 

 the general problem of visual space-percep- 

 tion. Two threads are so placed in a box 

 that they cross each other at an acute angle 

 while lying at different depths. If one of 

 the points of crossing be properly fixated, 

 two phantom threads will be seen passing 



planation applied to optical illusions the 

 following theories only will be considered: 

 namely, the contrast theory, the perspective 

 theory and the physiological theory. Lipps' 

 aesthetic theory must remain unconsidered 

 here, its unique form demanding rather a 

 particular treatment by itself. Let us see 



O 



between the main threads and making with 

 each other a figure which, if viewed from 

 the side, would resemble an X. The direc- 

 tions necessarj- for satisfactorily securing 

 the proper conditions for this illusion are 

 too detailed to find a place here. The in- 

 terested reader is, accordingly, referred to 

 the article designated in the foot-note.* 



Such are the principal illusions that are 

 being ardently discussed at the present time. 

 To mention the numberless variants and 

 minor illusions of form and magnitude that 

 have come to light in the course of these 

 discussions would be far beyond the scope 

 of this article. The reader who cares to 

 pursue the subject further is referred to 

 the literature of the subject, particularly to 

 Sanford's ' Laboratory Course in Psychol- 

 ogy,' where maj^ be found an excellent 

 bibliography practically complete to the be- 

 ginning of the current year. 



B. 



In attempting a brief summary of the 

 discussions relative to the principles of ex- 

 *C. H. Judd, Psych. Rev., V. (1898;, 286. 



how each of the three mentioned deals 

 with the overestimation of acute angles. 

 The contrast theory says that the two legs 

 of an acute angle are in a relation of mu- 

 tual antagonism, each point of one exerting 

 a repelling influence, as it were, upon a 

 point of the other. The consequence is, of 

 course, that the whole angle appears larger 

 than it really is. The perspective theory 

 asserts that acute angles are not overesti- 

 mated when unaccompanied with accessory 

 lines formed by the prolongation of the legs 

 of the angle, or otherwise. Then, and only 

 then, the lines are regarded as perpendicular 

 lines seen in perspective, and the acute 

 angle gains therefrom an increment of mag- 

 nitude. The physiolocjical theory, by which 

 that of Wundt is meant, claims that the 

 relative magnitudes of angles depend upon 

 the relative intensities of the muscular sen- 

 sations gained by sweeping the eyes over 

 the angle ; and since for acute angles there 

 is relatively more energy involved in the 

 starting and stopping of the movements of 

 the eyes, an acute angle, as compared with 

 an obtuse, must be relatively overestimated. 



