12 



KNOWLEDGE • 



[Nov. 4, 1881. 



tho strip OH are rrasod, tho illusion cc-nsps. The erasure 

 rcstorpK, as it were, the Npaci- (ill to the level of the [laper 

 to which it really Ix'longs. 



The ease illustnited in Fi>;. 1 is coininiiiily repirded (l)ut 

 without sufficient reiuson, or, inileed, any as-signed reason) 

 a-s belonging to the clas.s of illu.sions illustrated in Fig. 4 

 (first noticed liy ZUllner). Here the lines AB, CD, EF, 

 (HI, itc, which are really parallel, appear to converge alter- 

 nately towards AC', 1)F, Ed, IIL, and KM. This illusion 

 is ditierciit from that of Fig 1, as affecting the apparent 

 directions of lines, whilst the other does not (parallel lines 

 are regarded liy geometricians as in the same direction). 



Fig. 4. 



Tlie illusion of Fig. 4 appears to result from the 

 attention being drawn unduly to the circumstance 

 that the vertical lines pass athwart the other sets 

 at an angle, so that the angle is, as it were, exag- 

 gerated. The eye notices, for instance, that AB passes 

 the parallels in order from right to left, the uppermost 

 parallel crossed by AB l>eing farther to the right than the 

 lowest, and thus the idea is conveyed that B, instead of 

 being a point vertically below A, is to the left of such a 

 point. So D seems to the right of a point vertically below 

 C, and so on. 



The illusion of Fig. 4 admits of being varied and, in 

 some cases, strengthened by substituting wairdng lines of 

 various forms for the diagonal hatching. Several cases of 

 this kind will be shown m the ne.\t number. I conclude 

 this paper with a few simple illusions, afiecting not only 

 the direction and position of lines really straight, but also 

 their straightness, making them appear as curved lines. 



The lines AB, CD 

 of Fig. 5 appear to be 

 curved so as to be 

 nearer at the middle 

 than at either end ; 

 while the lines EF, 

 (JH, in the same 

 figure, appear to be so 

 curved as to be farther 

 apart in the middle 

 than at either end. 

 Obviously, the eye un- 

 consciously notes the 

 varying distance be- 

 tween the really curved lines and the straight lines, and 



attribute* part of the change of distance to a curvature of 

 the really straight line-s. 



This form of illusion may he modified, as Bhown in Fig. 6. 

 Some find the apy)arei]t curvature produced by the arrange- 

 ment of Fig. G stronger than the other. For my own 

 part, I find the apparent curvature of the lines AB, CD 

 strongest in Fig. 5, that of the lines EF, GH Btrongest in 

 Fig. 6. 



'I"he illusion seems 

 intensified in the case 

 of lines AB (Fig 7), 

 which seem to be 

 convex towards each 

 other ; the symmetry 

 of the pair of curves 

 lying V)etween these 

 parallels ought theo- 

 retically to restore the 

 idea of parallelism. 

 The lines EF and 

 («H in the same figure may be made to seem either parallel 

 or concare toward each other, according as the eye takes 

 together the cur\'es which approach EF and GH (re- 

 spectively) nearest, or the concentric pairs ; for the two 

 curves which lie between EF and GH produce opposite 

 elTects on each of the line'; EF, GH. 



Kit'. C. 



Kext week I shall consider other cases of apparent 

 curvature, but in the meantime I may note that I shall 

 be glad to hear from readers who have noticed illusions 

 akin to these, or may have been led to other explanations 

 than those I hare suggested. 



What is a man, 



If his chief good, and market of his time, 



Be but to sleep and feed ? A beast, no more. 



Sure, He that made us with such large discourse. 



Lookin;; before and after, gave us not 



That capability and godlike reason 



To fust in us unused. — Shakespeare. 

 Electiuc.^l ExniPiTioxs axd the Govek.xmeut. — Our corre- 

 spondent probably reflects the general opinion of British cxliibitors 

 in Paris when he says that " the conduct of oui- Government has 

 prevented our country from holding the place it deserved to hold 

 among European nations in an industry which promises before long 

 to be one of the utmost importance." But it is perfectly well 

 known to foreigners, and also to ourselves, that the British exhibi- 

 tor, so to sjieak. must swim without corks, lie m.iy not make so 

 large a show as some of his rivals ; but what lie does show is evem 

 more likely to be over-estimated, as being the result of his unaided 

 efforts, than to bo undervalued in consequence of any unfair com- 

 parison with those who have enjoyed advantages which he does not 

 possess. The difference between the conditions which surround 

 British and foreign exhibitors is thoroughly understood by all who 

 are interested in understanding it ; and we do not believe that a 

 steady adherence to the general rule of Government non-interven- 

 tion, although it may detract from the prettiness or completeness of 

 a display, will ever be really detrimental to the interests of a 

 national manufacture. — rimes. 



