1825.] ^^ Optical Deception, * *' " ' -^ • . "^ III 



will be in the position O a ; wli«n the former is at B, the latter 

 will be at O /3, and so on. 



Again ; let us suppose that when the aperture is just passing 

 the centre, the radius should be found in a certain position on 

 the other side OY, and rising towards the summit. Then tracing, 

 as before, the intersections of these lines in their progress, we 

 shall obtain a curve precisely similar to the former. Its position 

 will be reversed ; but its convexity will still be downwards. 



If the impressions made by these limited portions of the seve- 

 ral spokes follow one another with sufficient rapidity, they will, 

 as in the case of the luminous circle already alluded to, leave in 

 the eye the trace of a continuous curve line ; and the spokes will 

 appear to be curved, instead of straight. 



The theory now advanced is in perfect accordance with all the 

 phsenomena already detailed, and is farther confirmed by extend- 

 ing the experiments to more complicated combinations. 



It readily explains why the image, or spectrum, as it may be 

 called, of the spoke^ is at rest, although the spoke itself be 

 revolving: a circumstance which might escape notice, if the 

 attention were not particularly called to it, * 



Since the curved appearance of the hnes results from the 

 combination of a rotatory, with a progressive motion of the 

 spokes, in relation to the apertures through which they are 

 viewed, it is evident that the same phaenomena must be produced 

 if the bars be at rest, and both kinds of motion be united in the 

 wheel itself. For, whether the bars move horizontally with 

 respect to the wheel, or the wheel with respect to the bars, the 

 relative motion between them, and its effects, in as far as con- 

 cerns the appearance in question, must be the same. The atten- 

 tion of the spectator should in both cases be wholly directed to 

 the wheel, so that the motions in question should be referred 

 altogether to it. Thus, in fig. 4, the real positions, at successive 

 intervals of time, of the spoke A a, when the wheel is rolling on 

 the ground in the direction AZ, are expressed by the hnes Aa, 

 BZ>, Cc, and Dd, While the spoke is in these positions, the 

 portions of it really seen through the fixed aperture VW, are the 

 parts a, /3, 7, d, the impressions of which, being retained upon 

 the retina, and referred to the wheel when in its last position, 

 form the series of points m, n, p, and q, in the curved spectrum 

 7ri D. 



That the attention may the more Easily follow the wheel in its 

 progression, it is necessary that its circumference be distinctly 

 seen, and its real situation correctly estimated. Hence, although 

 it be true, that by a sufficient exertion of attention the pheenome- 

 non may be exhibited by means of a single aperture, it is much 

 more readily perceived, when the number of apertures is such as 

 to allow the wheel to be seen in its whole progress. For this 

 reaso4 the phsenomenon is very distinct in the case of a pahsade. 



