816 



SCIENCE. 



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



familiar as this figure is, discussions in re- 

 gard to tlie principles that should be applied 

 to its explanation are by no means at an 

 end. Two theories, especially, are at pres- 

 ent contending for the primacy : the one, 

 namely, falling back upon the supposedly 



fundamental principle that when acute and 

 obtuse angles come together in the field of 

 view the former are relatively overesti- 

 mated, the latter underestimated ; the other 

 appealing to pei-spective principles and 

 calling attention to the fact that the above 

 figure is to be seen, not as lying wholly in 

 the plane of the paper, but as presenting, 

 ■elevations and depressions, projecting ends 

 of lines and well-defined ridges. The first 

 theory is well enough understood to render 

 extended comment unnecessary. Suf&ce it 

 to say that the main lines, rather than the 

 short transversals, are affected by this false 

 estimation of angles for the very obvious 

 reason that they form in each case the com- 

 mon side of a multitude of angles. For a 

 long time this theory was content to stand 

 in this simple form. But the plastic phe- 

 nomena of the figure, which we shall have 

 to consider in a moment, are to-day too 

 evident to be lightly disregarded. Hence 

 the most recent statement of this theory* 

 takes full account of the prospective phe- 

 nomena present, but relegates them to a 

 secondary position, making them dependent 

 *Wiindt., Op. oit. 



upon the already present deflections of the 

 main lines. 



In sharp contrast to this are the claims 

 of the second theorJ^ For it perspective in- 

 fluences are primary and all-sufBcient. The 

 observations, made long ago by Hering and 

 Guye, to the effect that a careful attention 

 to the figure will i-eveal unmistakable plastic 

 characteristics, are here again emphasized. 

 Especially if the above figure be drawn 

 upon glass and viewed against a uniform 

 background, the tri-dimensional properties 

 become clearly apparent.* Not only do 

 the ends of the main lines run alternately 

 above and below the plane of the drawing, 

 but, further, the transversals seem so to slope 

 that if prolonged they would meet in ridges 

 similarly above and below the plane. Ac- 

 cordingly, the illusion is due to the interpreta- 

 tion that we give the figure. We see the 

 actual parallels projected, as it were, upon 

 the surfaces of solid and hollow prisms 

 which lean away from the vertical, and the 

 lines being actuallj' parallel the observer 

 must interpret the more remote ends as 

 diverging, as would actually be the case in 

 ordinary perspective vision. In other and 

 more general terms, the preponderatingly 

 tri-dimensional character of all our visual 

 experience compels us to interpret in the 

 light of this every perspective motive that 

 any linear drawing may contain. In the 

 figure before us the arrangement of lines re- 

 calls by association certain real experiences 

 with similar elements, and forthwith all the 

 attributes that would be given to the lines 

 and parts of a real seen object are given to 

 the linear drawing, even though the ob- 

 server be not consciously aware of anything 

 beyond the final perception which turns out 

 to be illusory. 



Such in mere outline are the two oppos- 

 ing theories which to-day seem likely to 



* The observer should always remember that the 

 perspective elements of any figure are most clearly 

 seen when one eye only is used. 



