of the Permanence of Impressions on the Retina. 4-41 

 in an angle less than that which has for measure the fraction 



1 



^+1 



V 



This is what has been done, for example, in the published 

 anorthoscope, with regard to the figure which represents a 

 lady holding a parasol. If the drawing exceeds the angle in 

 question, the distorted figure will be found folded upon itself 

 in such a manner that one of its extremities partly conceals 

 the other, and each of the regular figures produced will have 

 one of its extremities partly concealed by the other extremity 

 of its adjoining one. This, for example, may be seen in the 

 published anorthoscope, with respect to the figure representing 

 a galloping horse. It is clear that it will be usually advan- 

 tageous to arrange matters in this manner. 



Lastly, we have hitherto reasoned on the hypothesis in 

 which the black disc should present only a single slit ; but it 

 is easy to show that a number of equidistant slits may be 



pierced in this disc equal to the relation yj—. In fact, if we 



take again as initial positions of the two discs those in which 

 one slit corresponds to the first point of the distorted figure, 

 it is evident that, after one revolution from this point, the slit 

 will have made a portion of a revolution measured by the 



fraction :^; now, if at this moment a second slit comes be- 



fore the point in question, the regular figures produced by the 



latter will necessarily be superposed upon the first. As many 



slits, then, may be pierced in the black disc as the times that 



Vrf 

 the above fraction is comprised in unity, that is to say -^j— slits, 



it always being understood that this latter quantity is a whole 

 number. It is thus that, in the published anorthoscope, for 



* Vrf 



which we have y— =4, the black disc presents four slits. 



' n 



II. Velocities in the same direction. 



Let « and /3, as before, be the angles described at the same 

 time, starting from the vertical, by a slit and by a radius r of 

 the transparent disc, and let also i^ be the radius before which 

 the slit comes in its second position. The angle « will still 

 be that comprehended, in the regular image, by the two series 

 of points respectively ranged upon the radii r and /•'; but here 

 the angles « and /3 being on the same side of the vertical, the 



Phil, Mag. S. 3. Vol. 36. No. 245. June 1850. 2 G 



