298 On a Peculiar Class of Optical Deceptions. [1831. 



fectly fixed (fig. 10), and which, to the mind, offer a singular 

 contrast to the rapidly moving state of the wheels, and to the 

 variations which their velocity may undergo without altering 

 the visible result. 



This effect, strange as it at first appears, will be easily under- 

 stood by reference to fig. 9. Suppose the eye directed to the 

 part I beyond the cogs, and the sets of cogs to be moving with 

 equal velocities in the opposite directions, indicated by the 

 arrow heads : the part I will be eclipsed by the cogs a and b 

 simultaneously, and for exactly the same time, for they begin to 

 cover it and they leave it together ; / therefore is alternately 

 open to and shut from the eye for equal times ; for what these 

 cogs have done, will be performed by all the other cogs in turn, 

 and the cogs are equal in area to the spaces between : half the 

 light, therefore, from that part of the background comes to 

 the eye, and produces a corresponding impression. But with 

 respect to the point d, although the cog b is just leaving it ex- 

 posed, the cog a is just beginning to eclipse it ; and by the time 

 the latter has passed over, the edge of the cog e will be upon 

 the spot, and that cog will therefore hide it until f comes up; 

 so that in fact the point d is always hidden, no light comes from 

 that part of the background, and it consequently appears dark 

 V is circumstanced just as / was, for the cogs a and e cover 

 it simultaneously, and so do all the other cogs in pairs ; it is 

 therefore a light space in the spectrum : d 1 is a repetition in 

 everything of d, and is a dark space. The parts intermediate 

 between the maxima of light and darkness will, by examination, 

 be found to be eclipsed for intermediate periods, and to appear 

 more or less dark in consequence, so that the appearance of the 

 spectrum belonging to the visually superposed parts of the two 

 sets of cogs is as in fig. 10. 



In the case of equal wheels with radii, the fixed spectrum 

 produced when the wheels superpose each other has twice the 

 number of radii of either wheel, that being of course the num- 

 ber of times which the radii coincide with each other in one 

 revolution. Fig. 11 represents the fixed spectrum produced 

 by two equal wheels of eight radii each. When the radii or 

 spokes are narrow, the difference in the intensity of tint be- 

 tween the middle and the edges of each image of a spoke is so 

 slight as to be scarcely perceptible. But as this circumstance 



