of the Permanence of Impressions on the Itetina. 437 



slon to the two velocities, their relative direction, and the form 

 of the slits. In the instrument as constructed according to 

 my directions for the public, the velocity of tiie transparent 

 disc is to that of the opake disc as 4 to 1, and these velocities 

 are in opposite directions ; lastly, the slits are straight, and 

 directed from the centre of the disc to the circumference. 



With these elements, as shown by the instrument in ques- 

 tion, the distorted figure is single, it is angularly dilated, and 

 it gives rise to five regular figures symmetrically arranged 

 around the centre of the disc; but it is clear that other ar- 

 rangements would lead to other results. Now as no one, that 

 I am aware, has hitherto varied these arrangements, and as, 

 on changing them in part, we arrive in certain cases at results 

 which appear to me curious, I proceed to examine the subject 

 in some detail. 



To simplify the considerations, I will suppose the slits ex- 

 cessively narrow, so that they may be regarded as simple lines. 

 This being laid down, I shall here call to mind that the re- 

 gular figure obtained by the simultaneous movement of the 

 two discs is composed of the aggregate of the impressions left 

 on the eye by the points of the distorted figure seen through 

 the same slit in the successive positions of the latter. Now, 

 if the slit is considered in one of these positions in particular, 

 all the points of the distorted figure which correspond to it at 

 that instant presented to the eye, are perceived simultane- 

 ously, and consequently belong, with their relative positions, 

 to the regular figure ; that is to say, they are in the latter 

 ranged identically in the same manner upon a line of the same 

 form as the slit. Reciprocally, then, if, after having drawn 

 upon a sheet of paper the regular figure which it is desired to 

 reproduce by means of the apparatus, a line be traced upon 

 the latter which represents the slit in one of its positions, all 

 the points in which this line will cut the figure should be found 

 placed identically in the same manner upon a similar line in 

 the drawing of the distorted figure; and the same will take 

 place with any number of similar lines, traced upon the draw- 

 ing of the regular figure, and representing so many successive 

 positions of the slit. The series of points which are found 

 respectively upon these lines, will then have all their identical 

 corresponding points upon the drawing of the distorted figure; 

 but these last will not occupy among them the same relative 

 positions as upon the first drawing, and in this will consist the 

 deformation. 



To fix our ideas and avoid complication, let us suppose, in 

 what follows, that the slits are rectilinear, and directed ac- 

 cording to the radii of the disc. This being the case, we 



