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LXXV. On some new and curious applications of the Permanence of 

 Impressions on the Retina. — Third Note. By M. J. Plateau*. 



IN order to give, by means of the phantascope or phenakisti- 

 cope, the appearance of life and motion to the figures repre- 

 sented, it is requisite to hold the rotating disc very near to one 

 of the eyes, the other being closed, and to look through the zone 

 of the apertures at the image of the disc in a mirror ; this plan 

 is inconvenient, and moreover, it shows at once the whole series 

 of figures symmetrically arranged on the surface of the disc, and 

 consequently under every inclination, I shall now describe a mo- 

 dification of the apparatus, by means of which the eff"ect may be 

 observed directly, by both eyes, and by more than one person at 

 a time ; a modification which, moreover, exhibits the figures only 

 when in a suitable position, and which, lastly, much increases the 

 illusion. This modification consists in a combination of the 

 processes of the anorthoscope and the phenakisticope. 



Let us return to the first of these two instruments (see the 

 preceding Note, Phil. Mag. for June 1850), and suppose the 

 velocities of the two discs to be in a contraiy direction to each 

 other. Then, as we have shown in that Note, if by V^ is de- 

 noted the velocity of the disc with the distorted figure, and by 

 V„ that of the black disc, the relation between the corresponding 

 angular dimensions in the distorted figure and in the perfect 



figure, is equal to ^^^^ — h 1 • We have sho^sai that if the relation ^ 



» n ' n 



is not an entire number, the image produced in one revolution 

 of one of the slits is not superposed on the image which has 

 been produced in the preceding revolution of the same slit. But 

 this non-supei-position, which must necessarily be avoided in the 

 anorthoscope, constitutes, on the contraiy, one of the principles 

 of the illusion now in question. 



Let us take Vrf = l, and V„ = 4; in other words, let us sup- 

 pose that the black disc revolves four times faster than the trans- 

 parent disc. Tlie relation of the angular dimensions will then 

 be equal to ^ -j- 1 = |, and consequently the total angular width 

 of the distorted figure will Ije to that of the regular figure as 5 

 to 4'. Let us (haw the perfect figure in an angle occupying 

 j'^ of the circumference, which, according to the above value of 

 the relation between the angular dimensions, will give j^ for the 

 measure of the angle which the distorted figure should occupy. 

 This being done, let us trace upon a piece of paper a circle of 

 the same diameter as the transparent disc, and divide this circle 

 into twenty equal angles ; then let us draw a regular figure in 

 one of these angles, a second perfect figure in the following 



* From the Bulletin de I'Acad. Royale de Belf/ir/ue, vol. xvi. No. 7- 



