822 



SCIENCE.. 



[X. S. Vol. VIII. No. 206. 



end of the principal lino of A, and similar 

 tendencies to fall short of the ends of the 

 line in B, bring it about that the vertical of 

 A is perceived as the longer. This will be 

 true whether the eyes move freely along 

 the line or remain fixated upon some point 

 placed midway between the two figures Ij^- 

 ing side bj' side. In the latter case the il- 

 lusion will be diminished in amount, 

 though still existing, by reason of the fact 

 that there can still be weakened impulses of 

 the same kind as when the eyes are in mo- 

 tion. 



A quantitative studj^ of this illusion has 

 shown that for each angle made by the two 

 obliques a maximum of illusion is reached 

 with a particular length of oblique, on 

 either side of which the illusion diminishes. 

 Thus, if the principal line be of 75 mm. and 

 the angle between the obliques be 60 ° the 

 maximum illusion occurs when the length 

 of the oblique equals 30 mm.* 



Innumerable forms can be given to the 

 Miiller-Lj'er figures. The obliques may be 

 replaced by fork-like ends with parallel 

 prongs, or by circles and semicircles. Or 

 A and B of Fig. 5 may be placed end to end 

 in such a way that the outward pointing 

 obliques of A become the inward pointing 

 obliques of B, and in this condition various 



that of B, though they are of equal length. 

 Again, the point of bisection of the altitude 

 of an isosceles triangle seems placed too 

 high, the angle of the vertex acting ap- 

 parently in the sense of B, of Fig. 5. Type 

 founders have taken account of this in 

 placing the horizontal of the letter A far be- 

 low the middle. 



4. Munsterherg'' s Illusion of the ' Shifted 

 Checker-board Figure.' The illusion of Fig. 

 8* differs essentially from all the foregoing, 

 for while it resembles the Zollner pattern 

 in the converging and diverging character 

 of the vertical lines its explanation rests 

 upon a totally different principle, namely, 

 tha,t oi irradiation. Fig. 8 may be called 'the 

 illusion of the kindergarten patterns, ' since 

 it reproduces in black and white the type 

 of patterns used in the occupation of mat- 

 weaving. A single element of the illusion 

 may be obtained by taking from the figure 

 one of the vertical lines and the several 

 pairs of overlapping rectangles that lie 

 along it. If, further, the rectangles be 

 changed to squares we have the form of 

 the illusion first published by Professor 

 Miinsterberg only a few years ago in the 

 Milton Bradley collection entitled ' Pseud- 

 optics.' The brief assertion was there 

 made that the illusion is due lo irradiation. 



B 



combinations of obliques may be omitted 

 without destroying the illusion. Many 

 more complex figures may be constructed 

 which display illusions due to the presence 

 of Miiller-Lj^er motives. Fig. 7 shows two 

 of these, the side A appearing longer than 



* Heymans. Zeitsoli. f. Psyob., etc., IX., 227. 



This statement, however, German writers 

 have shown themselves singularly disin- 

 clined to adopt. Heymansf and LippsJ 



* The illusion may be best seen by holding the dia- 

 gram somewhat beyond the range of most distinct 

 vision, or by viewing it as reflected in a mirror. 



t Heymans. Loc. cit. 



J Lipps. Op. cit., p. 319. 



