On the Permanence of Im^resuom on the JRetina, 435 



conveniently placed behind the coloured disc; lastly, the ob- 

 server must also place himself on the other side of the appa- 

 ratus, that is to say, opposite to the black disc, keeping his 

 eyes on a level with the centres of the discs, whilst another 

 person turns the handle with sufficient rapidity. The di- 

 stance of the observer from the apparatus must be a metre at 

 least. 



With this arrangement, let us imagine, for an instant, that 

 the diameters of the two brass pulleys are mathematically 

 equal, that the same is the case with the two wooden pulleys, 

 and that the thicknesses of the two cords are also exactly 

 alike. Then the velocities of the two discs will be perfectly 

 equal ; and as they are in the same direction, it is clear that 

 if, at the commencement of the movement, the two openings 

 correspond, for example, to the red sectors, they will continue 

 to correspond with them indefinitely ; so that, if the velocity is 

 sufficient, the observer will simply see the whole circular 

 space traversed by the openings^ coloured a uniform red, and 

 the effect of the apparatus will be limited to this. But this 

 perfect equality of the velocities will not be realized; for sup- 

 posing the pulleys to have been made with such care that 

 their diameters might be regarded as perfectly equal, and 

 admitting moreover that the two cords, taken from the same 

 piece, have exactly the same thickness, special precautions 

 would still be requisite for them to have exactly the same 

 tension ; and a very small difference in this respect suffices to 

 alter in some degree the equality of their thicknesses, and con- 

 sequently that of the velocities. There will therefore be in 

 general a small inequality between the velocities of the two 

 discs, and upon this inequality is founded the illusion here in 

 question. 



In fact, let us suppose, in order to fix our ideas, that the 

 colours are ranged in the order of figure 1, that the discs turn 

 in the direction indicated by the arrows, and that the black 

 disc has a small excess of velocity. In this case, let us arrange 

 matters so that before putting the apparatus in motion, the 

 middle of the width of the openings may correspond with the 

 middle of that of the black sectors of the other disc. It is 

 then clear that at the commencement of the movement the 

 observer will only see a completely black surface. But the 

 relative position of the openings and of the black sectors 

 changing by degrees, by reason of the small excess of velocity 

 of the first, after a certain time the openings will begin en- 

 croaching a little upon the red sectors, and consequently the 

 observer will see the black surface become uniformly coloured 

 with a slight tinge of red; then the encroachment of the 



