lOS Dr, Roget's Explanation of ^ [AtC. 



rally do if no bars intervened, seem to have a considerable degree 

 of curvature. The distinctness of this appearance is influenced 

 by several circumstances presently to be noticed ; but when 

 every thing concurs to favour it, the illusion is irresistible, and, 

 from the difficulty of detecting its real cause, is exceedingly 

 striking. 



The degree of curvature in each spoke varies according to the 

 situation it occupies for the moment with respect to the perpen- 

 dicular. The two spokes which arrive at the vertical position, 

 above and below the axle, are seen of their natural shape, that 

 is, without any curvature. Those on each side of the upper one 

 appear slightly curved ; those more remote, still more so ; and 

 the curvature of the spokes increases as we follow them down- 

 wards on each side till we arrive at the lowest spoke, which, 

 like the first, again appears straight. 



The most remarkable circumstance relating to this visual 

 deception is, that the convexity of these curved images of the 

 spokes is always turned downwards, on both sides of tne wheel; 

 and that this direction of their curvature is precisely the same, 

 whether the wheel be moving to the right or to the left of the 

 spectator. The appearance now described is represented in 

 PlateXXXVI.fig. 1.* 



In order to discover a clue to the explanation of this phaeno- 

 menon, it was necessary to observe the influence which certain 

 variations of circumstances might have upon it ; and the follow- 

 ing are the principal results of the experiments I made for this 

 purpose. 



1 . A certain degree of velocity in the wheel is necessary to 

 produce the deception above described. If this velocity be 

 gradually communicated, the appearance of curvature is first 

 perceptible in the spokes which have a horizontal position : and 

 as soon as this is observed, a small increase given to the velocity 

 of the wheel, produces suddenly the appearance of curvature in 

 all the lateral spokes. The degree of curvature remains precisely 

 the same as at first, whatever greater velocity be given to the 

 wheel, provided it be not so great as to prevent the eye from 

 following the spokes distinctly as they revolve : for it is evident, 

 that the rapidity of revolution may be such as to render the 

 spokes invisible. It is also to be noticed that, however rapidly 

 the wheel revolves, each individual spoke appears, during the 

 moment it is viewed, to be at rest. 



2. The number of spokes in the wheel makes no difference in 

 the degree of curvature they exhibit. 



3. The appearance of curvature is more perfectly seen when 

 the intervals between the bars through which the wheel is 



♦ The appearance in question has been noticed by an anonymous writer in the Quar- 

 terly Journal of Science (vol. x. p. 285i), who gives, however, no explanation of the 

 phenomenon. It would have been impossible, indeed, to reconcile the facts as they are 

 there statetl, with any theory that could be iqaagined for tlieir solution. 



