i70 Explanation of an Optical Dcccptio?}, 



tion of the curved images of the spokes ; but if a certain rela- 

 tion 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 genei'al 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 those 

 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 mo- 

 tion. 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 progi-essive mo- 

 tion be given to the bars while the wheel revolves round a 

 fixed axis, the spokes immediately assume a curved appear- 

 ance. 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 circum- 

 stance of separate parts onlj' 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 aper- 

 tures, it is not so easy to understand why they do not connect 

 themselves in ythe imagination, as in other cases of broken 

 lines, so as to convey the impression of a straight spoke. The 

 idea at first suggests itself, that the portions of one spoke, thus 

 seen separately, might possibly connect themselves with por- 

 tions of the two adjoining spokes, and so on, forming by their 

 union a curved image made up of parts from different succes- 

 sive spokes. But a little attention to the pha'uomena will show 



that 



