of the Permanence of Impressions on the Retitia. 44-5 



torted figure can occupy ; then, as I have said, this figure 

 will have been crossed entirely by the slit. 



According to this, since the slit will only be found in coin- 

 cidence with the commencement of that angle after V„— 1 

 new revolutions, it follows that, during these, it will pass 

 before the free part of the disc, and that nothing longer 

 will be seen ; then, that a second regular figure will be pro- 

 duced in a position identical with the first, to be followed by 

 a new interval in which nothing will be seen, and so on. 

 This would constitute a serious inconvenience, did not a very 

 simple means present itself to obviate it. This means consists 

 in dividing the transparent disc into V„ equal angles, and re- 

 peating, in each of them, the drawing of the distorted figure. 

 Then, in fact, it is clear that after each of its revolutions, the 

 slit will coincide with the origin of one of these angles which 

 it will sweep entire in the following revolution, so that the 

 regular images will be produced without interruption, and 

 will all be mutually superposed. Another advantage will 

 hence result ; that in general the anamorphosis will be much 

 more difficult to decipher. Thus, whilst for velocities in op- 

 posite directions the distorted figure is single and the regular 

 image multiple, it is the contrary in the case which we are 

 examining ; that is to say, the distorted figure is multiple and 

 the regular image single. 



Lastly, let us seek what number of slits may be pierced in 

 the black disc. For each of these slits to produce identically 

 the same effect, it will suffice that when, after a coincidence 

 between one slit and the first point of one of the distorted 

 figures, the first point of the following distorted figure shall 

 reach the same spot, another slit is come before it. Now, 

 from one of these two positions to the other, the transparent 



disc has moved over an angle measured by the fraction y-; 



and as the angle, the slit of which has turned at the same 

 time, is to the preceding one in the relation of the velocity of 

 the black disc to that oi' the transparent disc, this angle will 



evidendy have for measure the fraction ^-. Such, then, is the 



valueof the angle by which the second slit should be removed 

 from the first; and as the same thing will take place with re- 

 gard to the third slit in relation to the second, and so on, it is 

 clear that the total number of the slits will be equal to V^. 



We will illustrate all this by an example. Let us suppose 

 that the velocity of the transparent disc is to that of the black 

 disc as 3 to 4, numbers which satisfy the condition that we 

 have established, namely, only differing from each other by 



