156 THE TOP. 
while m is swinging through 180°, or in other words, the 
radius will be larger. 
Now we will apply this principle. Suppose our glass 
plate to be inclined a small amount to the horizon, the 
side toward us being the highest. Then as p passes on 
from A, the action of gravity will accelerate, the move- 
ment on the left hand half, and retard it on the other. 
The velocity due to gravity will be zero at A, greatest at 
A’, then diminishing back to zero at A again. 
The curvature of the path, since the rate of gy- 
ration is not affected, should diminish from A to A’, 
and increase from A’ to A. Hence the path should be 
flattest at A’, and round most rapidly at A, something 
like figure 4.’ 
_AAAA Ue 
A’A’ 
So strongly marked a loop form will occur only when 
the plate is considerably inclined. Such may be seen 
in plate III. 
Further consideration of these movements will show 
that as p ascends towards A, the curvature increasing as 
has been shown, the radius must become shorter in the 
same ratio, hence the point will not rise as high as the 
first A, hence the loops will grow smaller as the series 
extends. Hence, too, the instrument will gradually 
work its way towards the side on which the radii are 
erowing less. In the case before us where A is the 
highest (fig. 3), it will move towards the right, and its 
rate of movement will depend upon the inclination of 
the plane, the former growing more rapid as the latter 
increases. 
By availing oneself of this principle, it is easy to guide 
the top and send it to the right or left, or back and forth. 
1 This is copied from an actual tracing by my top, but does not adequately represent the 
exquisite regularity of the path. 
p 40 
