of the Permanence of Impressions on the Retina. 4-43 



form it afterwards, it may be taken quite arbitrarily as to 

 position and size, provided, be it well understood, that it is 

 comprised in a circle equal in diameter to the transparent 

 disc. This regular figure may, for example, be a head equal 

 in height to the diameter of the disc. Only, the pulleys to 

 which the discs are fixed, and the rod which bears these pul- 

 leys, will conceal a small portion of the image. The greatest 

 angle which the regular figure can occupy will then be mea- 

 sured by an entire circumference. Consequently, if we again 

 take the circumference for unity in the measure of the angles, 

 and designate by A the greatest angle which the distorted 

 figure can occupy, the equation (4.) will give, making y=l 

 and y' = A, 



A=M; (5.) 



thus the extent of the distorted figure cannot exceed an angle 

 having for measure the fraction M. 



Although one entire revolution of the slit can, as we have 

 seen, produce only a single regular figure, yet the figures which 

 are produced in the subsequent revolutions must be all super- 

 posed on the first, without which there would be confusion. 

 But this requires that the successive coincidences of the slit 

 and the first point of the distorted figure be effected at the 

 same spot; or, in other words, that in the interval of one coin- 

 cidence to the following, the slit make either one complete 

 revolution, or an entire number of revolutions. Let us then 



seek the condition which, for this to happen, the relation :yr- 



of the two velocities must satisfy. 



Let us suppose this relation reduced to its simplest expres- 

 sion, or, in other words, let us assume to represent the two 

 velocities, two numbers which have no common factor. As 

 in the case of the velocities of contrary directions, let a' be 

 the angle described by the slit from one coincidence with the 

 first point df the distorted figure up to the ensuing coincidence. 

 The mode of reasoning which we have employed to arrive at 

 the expression (2.), will lead us, in the present case, to the 

 relation 



which will give 



4-^)-. 



But as, from one coincidence to the other^ the slit must ac- 



2 G 2 



