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Some New Optical Illusions. 
The radius of the circle of imparted motion should equal the 
width of a black or of a white ring, and the rapidity found 
most successful is that when each rotation occupies from 
one-sixth to one-fourth of a second. The rings appear to 
rotate once for every complete motion of the hand and card 
in the circular path, and in the same direction as the im- 
parted motion. In this experiment each ring is displaced to 
a distance equal to its own breadth in every direction suc- 
cessively around its centre ; and as the impression remains 
a short time on the retina, the optical effeCt is equivalent to 
that of a ring eccentric to an equal amount and actually 
rotating. Hence the illusion. 
I have constructed a large number of patterns of curvilinear, 
circular, elliptical, eccentric, and concentric lines, many of 
which exhibit, in whole or in part, the same phenomena of ap- 
parent rotation. One of these is a single black circle, having 
a number of internal cog-teeth, upon a white ground. This 
circle, when shaken circularly in the manner described, ap- 
pears to move round in the opposite direction to the imparted 
motion, and to move round through a distance of but one 
tooth for each successive complete motion. For circles pos- 
sessing this property I have suggested the name of “ Strobic 
Circles.” Their motions are best seen when the eye is di- 
rected not exactly at the circles, but at some point near them. 
I have therefore found it more effective to have two strobic 
circles drawn side by side upon one card. That circle rotates 
most obviously on which the gaze is not fixed. 
Further, I have noticed that if a strobic circle be 
“ rotated,” while a number of other circles are lying sta- 
tionary within the field of view, when the eye was directed 
to the moving circle the others also began to “ rotate.” 
This last observation cannot, I think, be explained on any 
supposition of unconscious muscular movement. In faCt I 
entirely doubt the validity of this hypothesis in the case of 
Addams's observation upon the waterfall before cited. 
I am inclined rather to attribute these effects, and those of 
“ compensation ” in general, to waves of nervous disturbance 
moving over the retina ; these waves, being of two orders, — 
one primary, and in the same direction as the objective 
motion of the images upon the retina ; the other secondary 
and later in time, — giving rise to the subjective motions of 
compensation. I do not see how on any other supposition 
the phenomena noted in an earlier paragraph relative to 
compensative shrinking or expanding of objects can be ex- 
plained. Such a hypothesis, will, I believe, also embrace all 
the other phenomena of apparent motion, except those which 
