480 



SCIENCE. 



[N. S. Vol. VIII. No. 197. 



Toom, the illumination being furnished by the 

 •electric spark. The rotation of the disk will 

 seem to be now in one direction, now in the 

 other, according as any sector, made visible by 

 the instantaneous flash, is seen to occupy a 

 position on this or that side of the sector seen 

 just previously. If in addition any perceived 

 phase could admit of a double interpretation 

 we should have the illusion in question. 



The reason for the illusion may, perhaps, be 

 seen in this way. Fancy, for example, a nar- 

 row pennant floating from a staff, the observer 

 being so placed that the line of direction of the 

 pennant shall make an angle of, say, 30° with 

 the plane passing through the observer and the 

 staff. Further, let the pennant droop somewhat 

 from the horizontal. If, now, this be viewed 

 from a sufficient distance and by a somewhat 

 dim light, it will prove impossible to determine 

 absolutely whether the pennant is floating to- 

 wards or away from the observer. That is, we 

 have here a simple case of equivocal interpreta- 

 tion. The same double interpretation is true 

 for every pair of positions between those just 

 considered and the point where the pennant is 

 perpendicular to the plane above mentioned. 

 Suppose now that the pennant be made to 

 rotate about the staff", occupying successively 

 each of these positions. Manifestly the direc- 

 tion of rotation can not now be determined with 

 full satisfaction, for since each of the phases 

 seen was capable of a double interpretation, 

 their succession must give rise to a possible per- 

 ception of rotation in either of two directions, 

 either from a position more remote to one 

 nearer, or vice versa. Probably one direction 

 will always be selected as real over against the 

 other as illusory, for there are usually some 

 subordinate factors that are dimly perceived 

 which admit of only a single meaning. 



Here then we have a type of the illusion. 

 Now let the pennant be replaced by the vanes 

 of a windmill or by the blades of an electric 

 fan, and we find further equivocal factors pre- 

 sent. Take the latter case. Not only the direc- 

 tion of the rotation, but the slope of the blades 

 as well may be perceived in two ways. For 

 the patches of light and shade, on the basis of 

 which the slope is perceived, are also equivocal, 

 and the particular illusory perception that we 



get, not only of the direction, but also of the 

 plane of the rotation, depends upon the special 

 combination of these two equivocal factors. The 

 whole matter is then at bottom one of the per- 

 spective interpretation of successive perceptions 

 of light and color in their various combina- 

 tions. 



The above explanation is strongly substantia- 

 ted by the universally observed fact that the 

 rotating object must be viewed at a certain dis- 

 tance or by a dim light. That is, certain de- 

 tails which admit of but one meaning must be 

 suppressed before the illusion can arise. Again, 

 the fact that the illusion is at its best when the 

 rotating object is viewed very obliquely makes 

 for the explanation given. For here perspec- 

 tive interpretation is given full play. This 

 oblique position of the observer is, however, 

 not necessary in every case, for the writer has 

 repeatedly seen the illusion when viewing a 

 four-vaned windmill directly en face. Further, 

 this explanation is strengthened by the fact 

 that the illusion is most clear when one eye is 

 covered. 



Which one of the rotations shall in any given 

 case be seen, when either is equally possible, 

 will depend probably upon the position of the 

 eyes. This is influential in all equivocal per- 

 ceptions, and, as Wundt has pointed out, the 

 law seems to be that the point fixated appears 

 nearest to the observer. 



Attention may be called here to a somewhat 

 similar illusion mentioned by Silvanus P. 

 Thompson in the Quarterly Journal of Science 

 for 1879. If a crow be seen at dusk flying low 

 against the sky the wings, seen alternately 

 above and below, give the appearance of a 

 single wing rotating about the crow's body like 

 the blade of a screw propeller about its axis. 

 The points of similarity between this and the 

 Windmill Illusion are manifest. 



A. H. Pierce. 



Amheest College. 



Me. Kenyon's optical illusion described in 

 your issue of September 16th may be best ex- 

 plained by another illusion with which I have 

 been long familiar. 



Take an ordinary glass goblet, tilt it a little 

 from you, so that the farther rim is seen 



