136 Dr. Roget's explanation of 
through a single narrow vertical aperture which is moving 
horizontally in a given direction PQ. Let us also assume 
that the progressive motion of the aperture is just equal to 
the rotatory motion of th^ circumference of the wheel. It is 
obvious that if, at the time of the transit of the aperture, the 
radius should happen to occupy either of the vertical posi- 
tions VO or OW, the whole of it would be seen at once 
through the aperture, in its natural position ; but if, while 
descending in the direction VR, it should happen to be in an 
oblique position RO, terminating at any point of the circum- 
ference at the moment the aperture has, in its progress ho- 
rizontally, also arrived at the same point R, the extremity 
of the radius will now first come into view, while all the 
remaining part of it is hid. By continuing to trace the parts 
of the radius that are successively seen by the combined 
motions of the aperture and of the radius, we shall find that 
they occupy a curve ^ah c d generated by the continued 
intersection of these two lines. Thus, when the aperture has 
moved to A, the radius will be in the position O a ; when the 
former is at B, the latter will be at O /3, and so on. 
Again ; let us suppose that when the aperture is just pass- 
ing the centre, the radius should be found in a certain position 
on the other side OY, and rising towards the summit. Then 
tracing, as before, the intersections of these lines in their pro- 
gress, we shall obtain a curve precisely similar to the former. 
Its position will be reversed ; but its convexity will still be 
downwards. 
If the impressions made by these limited portions of the 
several spokes follow one another with sufficient rapidity, 
they will, as in the case of the luminous circle already alluded 
