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1831.] are furthest from the upper straight line. These curves are the same in form as those already described and explained by Dr. Roget, and the appearance itself is produced in a similar manner; but the phenomena are distinct and the causes different. The effect at present referred to is best observed when the velocities are great, whereas that explained by Dr. Roget takes place only when the velocities are moderate. It is probable that some of the appearances briefly mentioned by an anonymous writer in the 'Quarterly Journal of Science,' First Series, vol. x. p. 282, and already referred to by Dr. Roget,—were of the kind now to be explained; for though the description is not accurate either for the effects which form the object of this paper, or that explained by Dr. Roget, and is, indeed, inconsistent with the observation or explanation of any of the phenomena,—it probably had its origin in the occurrence of some of both kinds under the eyes of the writer. The effect is easily obtained by revolving a white pasteboard wheel before a black or dark ground, and then, whilst regarding the wheel fixedly, traversing the space before it with a grate also cut out of white paste hoard. By altering the position of the grate and direction of its motion, it will be seen that the straight lines in the wheel are always parallel to the bars of the grate, and that the convexity of the curved lines is always towards that side of the grate where its motion coincides in direction with the motion of the radii of the wheel. By varying the velocity of the wheel and grate, the curves change in their appearance, and the whole or any part of the system, as described and figured by Dr. Roget, may be obtained at pleasure.

I have had a very simple apparatus constructed, by which these and many other analogous appearances can be shown in great perfection and variety. One board was fixed upright upon the middle of another, serving as a base; the upright board was cut into the shape represented in fig. 4; the middle, and the two extreme projections, forming points of support, were supplied with little caps cut out of copper-plate and bent into shape (fig. 5), so that, when in their places, they offer four bearings for the support of two axes, one on each side the middle. The axes are small pieces of steel wire tapered at the