1825. J an Optical Deception, - 109 



viewed, are narrow ; provided they are sufficiently wide to allow 

 of the distinct view of all the parts of the wheel in succession, 

 as it passes along. For the same reason, the phsenomenon is 

 seen to the greatest advantage when the bars are of a dark 

 colour, or shaded, and when a strong light is thrown upon the 

 wheel. The deception is, in like manner, aided by every circum- 

 stance which tends to abstract the attention from the bars, and 

 to fix it upon the wheel. 



4. If the number of bars be increased in the same given 

 space, no other difference will result than a greater multiplica- 

 tion of the curved images of the spokes ; but if a certain relation 

 be preserved between the angles subtended at the eye by the 

 whole intervals of the bars, and of the extremities of the spokes^ 

 this multiplication of images may be corrected. The distance 

 of the wheel from the bars is of no consequence, unless the 

 latter are very near the eye, as in that case the apertures^ 

 between them may allow too large a portion of the wheel to be 

 seen at once. 



5. If the bars, instead of being vertical, are inclined to the 

 horizon, the same general appearances result; but with this 

 difference, that the spokes occupying positions parallel to the 

 bars, are those which have no apparent curvature ; while the 

 curvatures of the other spokes bear the same relations to these 

 straight spokes, and to each other, that they did in the former 

 case. When the inclination of the bars is considerable, how- 

 ever, the images become more crowded, and the distinctness of 

 the appearance is thereby diminished. The deception totally 

 ceases when the wheel is viewed through bars that are parallel 

 to the line of its motion. 



6. It is essential to the production of this effect, that a com- 

 bination should take place of a progressive with a rotatory 

 motion. Thus, it will not take place if, when the bars are sta- 

 tionary, the wheel simply revolves on its axis, without at the 

 same time advancing : nor when it simply moves horizontally 

 without revolving. On the other hand, if a progressive motion 

 be given to the bars, while the wheel revolves round a fixed axis, 

 the spokes immediately assume a curved appearance. The 

 same effect will also result if the revolving wheel be viewed 

 through fixed bars by a spectator^ who is himself moving either 

 to the right or left ; because such a movement on the part of 

 the spectator produces in his field of vision an alteration in the 

 relative situation of the bars and wheel. 



It is evident from the facts above stated, that the deception in 

 the appearance of the spokes must arise from the circumstance 

 of separate parts only of each spoke being seen at the same 

 moment; the remaining parts being concealed from view by 

 the bars. Yet since several parts of the same spoke are actually 

 seen in a straight line through the successive apertures, iti^ 



