76 GORHAM, ON THE 
ment, or that nearest to the circumference, is equal to 30, 
the second segment to 60°, the third to 90°, and so on to 
the eleventh, adding 30° to each segment. Now join the 
ends of these segments by a curved line on either side, and 
the curvilinear or heart-shaped appendage is completed. 
When such an appendage of pure white is affixed to a disc 
of black (fig. 12) and rapidly rotated, the mixture presents 
a soft transition from white to black, through an atmosphere 
of gray, which is most refreshing to the eye. Many agree- 
able transitions may be produced by using the white scale on 
grounds of blue, green, and red, in succession. A red scale 
on a ground of blue presents a most gorgeous picture—a 
pure red gliding imperceptibly into blue, through every 
conceivable hue of violet. 
MULTIPLIED FIGURES BY ROTATION. 
The Kaleidoscopic Colour-top. 
When two rotating discs are used in a particular manner, 
and placed in a particular position relative to each other and 
the eye, they constitute the Kaleidoscopic Colour-top, or an 
instrument for exhibiting beautiful forms which are similar 
to those of the kaleidoscope, although essentially distinct as 
to the principle on which they are constructed. Let a, for 
example, be a disc having the three primary colours, yellow, 
red, and blue, evenly distributed in sectors of 120° on its 
surface, and let this disc be fixed to the colour-top and 
rotated. Let B be a second disc, blackened on its upper sur- 
face, and having a central aperture somewhat larger than 
the spindle of the top, as well as a pattern of six or eight 
rays cut completely through and out of its substance, so that 
when held vertically over the disc a it will admit of the 
colours being seen through such pattern when viewed from 
above. If now the wheel is set in motion, and the dise B be 
allowed to drop down upon the spindle of the colour-top, 
it will be held in contact with the spindle by centrifugal 
force, and will revolve in a plane parallel with the wheel, in 
the same direction and with the same velocity. In this case 
the colours on A appear mixed, while the pattern on B 
is effaced. But if the motion of B is retarded, and at the 
same time broken up into a series of rapid and regular 
jerks, or more properly tsochronous vibrations, while the eye 
is held vertically over the spindle, each pattern is retained 
for an instant before the eye, yet sufficiently long to form a 
