SOME NEW OPTICAL ILLUSIONS. 
7 
best if the circles be clear and sharp at their edges, and the succes- 
sive rings of black and white of equal widths. Their number and 
width is immaterial, but there seems to be a particular distance 
from the eye for each width of successive rings, at which the 
illusion succeeds best. Finely-drawn narrow rings must be held 
near, to produce a maximum effect; while to enable a number 
of persons to see the illusion at once the rings may be half or 
three-quarters of an inch in width, and to the number of fifteen 
or twenty. 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 imparted motion. 
In this experiment each ring is displaced to a distance equal to 
its own breadth in every direction successively 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 apparent 
rotation. One of these (PL 2) 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, appears 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 possessing this property 
I have suggested the name of “ Strobic Circles.’^ Their motions 
are best seen when the eye is directed 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. 
