October 20, 1892] 



NA TURE 



591 



larger the angle the greater the deviation. Similar figures 

 with acute angles substituted for the obtuse ones would 

 show a scarcely perceptible illusion. (2) When obtuse 



angles formed by lines a and c with the vertical lines re- 

 spectively, deviate the lines a and c towards the direction 

 of the angles sufficiently to bring them in line with one 

 another. Fig. 6 adds the further complication — explicable 

 upon the same principles — that the line is deviated once 

 in one direction and then in the reverse direction. 



We have next to show that the illusion of deviation from 



angles are combined with acute angles, the deviating 

 effects of the former outweigh those of the latter. In 

 Fig. 4 the effect of the angle acd would be to make the 



ye 



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Fig. 9. 



j parallelism is similar to that from continuity. If the right- 

 hand portion of Fig. 3 be rotated through 1 80° and placed 

 I below the left-hand portion, we have Fig. 7, in which we 

 j observe a tendency for the two horizontal lines to diverge 

 on the left and converge on the right ; this is just what 

 our dictum demands. To strengthen this illusion we add 

 more oblique lines, and thus more angles, the obtuse 



I Fig. 5. Fig. 6. 



line AB if continued fall below fg, while the effect of 

 BCD would be to make AB fall above FG ; the former 



by the angle acd. The angle BCE reinforces acd, while 

 ACE reinforces BCD. Angles greater than 180° do not 

 come into consideration. When all the angles about a 



angles in all cases outweighing the acute ones— Fig. 8. 

 We have now only to draw two figures like Fig. 8, side 

 by side, and draw the oblique lines across the vertical ones 

 (thus keeping the figure compact) to obtain Fig. i, with 

 which we set out. The possibilities of illusion do not 

 stop here ; by drawing the oblique lines in one direction on 



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point are equal, i.e., are right angles, the illusion disap- 

 pears. Figs. 5 and 6 furnish other illustrations of the 

 same principles. In Fig. 5 the line a seems continuous 

 with c while it is so with b, and this because the obtuse 



NO. 1199, VOL. 46] 



Fig. II. 

 one side, and in the other direction on the other side, we 

 can deviate the two halves of the same pair of parallel 

 lines in opposite directions, as is done in Fig. 9 ; while 

 most striking of all is the elaborate design of Fig. 10, in 

 which it is difficult to realize that the four main Imes are 

 all straight and parallel. If the page be viewed with one 



