CHARLES B. WARRING. 155 
the various movements, all easily deduced from the ro- 
tation on the axis. 
Suppose that the top at the instant we begin to ob- 
serve it, is passing A. As m swings slowly to the right, 
the point’s path begins to curve to the left, and will con- 
tinue to curve just as m does, both completing 180° in 
the same time. If m’s motion around the instantaneous 
axis q, is uniform, the curvature of p’s path will 
also be uniform, and the ,path, a circle. If p re- 
volves on its axis very rapidly, it will travel forward 
very rapidly ; and since m’s rate of curvature (its gyra- 
tional movement) is proportionally slow, the rate of 
curvature of p’s path will be correspondingly slow; 
and the slower the curvature the greater the distance p 
will travel (roll along) to get through a quadrant. In 
other words, the radius of its path will vary directly as 
n, the number of revolutions which the top makes on its 
axis per second. 
If by any means the forward movement of p is dimin- 
ished, while the angular, or gyrational, movement of m 
remains unchanged, the radius of the path will grow 
smaller, since p will travel a less number of inches while 
m is Swinging around 180°; and, conversely, if the trans- 
lational speed is increased, p will travel more inches 
39 
