of the Permanence of Impressions on the Retina. 439 



we shall have 



M=^4-l, (1.) 



a quantity which depends only on the relation between the 

 velocities of the two discs. 



From the above it is seen, that, for a given relation between 

 the two velocities, the construction of the distorted figure will 

 be effected by the following process: — 1. Tracing upon the 

 drawing of the regular figure which it is desired to reproduce, 

 a series of radii sufficiently near together. 2. Tracing the 

 same number of radii upon the disc which is to bear the dis- 

 torted figure, but so that the angle comprised between each 

 of these latter radii and that which follows it be to the angle 

 comprised between the two corresponding radii of the regular 

 drawing in the relati(m M. 3. Transferring successively upon 

 each of the radii of the disc the series of points ranged upon 

 the corresponding radii of the regular drawing, placing these 

 points at the same respective distances from the centre. 

 4. Lastly, connecting with each other, by suitable lines, the 

 points thus distributed. For example, in the published anor- 

 thoscope, the velocity of the transparent disc is fourfold that 

 of the black disc, which gives M = 5; and, in fact, the con- 

 struction of the drawings of that instrument consisted simply 

 in rendering the angular distances five times greater than in 

 the regular figures which were to be reproduced. It is seen, 

 by the above general expression of the relation M, that the 

 deformation will be greater in proportion as the velocity of 

 the transparent disc is more considerable with relation to that 

 of the black disc. 



We may substitute, in the formula (1.), for the quantity M 



its equal ; hence we shall consequently have 



^+ 



"="(v:+0' 



an expression in which /S + a is evidently the angular distance 

 which separates the radius r of the slit, when the latter has 

 described the angle «. Now, if this latter angle is such that the 

 angular distance /S + a has for its measure the entire circum- 

 ference, the slit will occur again before the radius r. If, then, 

 we designate by a.' the value of a which fulfills this condition, 

 and if, in order to simplify, we take the circumference as unity, 

 the condition in question will give 



«'(^-) 



1, 



