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 understood by reference to fig. 9. Suppose the eye directed to the part l 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 l 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; l 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 exposed, 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 con equently appears dark -l' is circumstanced just as l was, for the cogs a and c cover it simultaneously, and so do all the other cogs in pairs; it is therefore a light space in the spectrum: d' 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 number 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 between the middle and the edges of each image of a spoke is so slight as to be scarcely perceptible. But as this circumstance
