154 THE TOP. 
e. g., 90°, will depend upon the size of the ‘‘ point,”’ the 
rate, n, at which the top revolves on its axis, and the 
slowness of m’s movement, 7, e., the slowness of the 
gyration. 
Hence, since the size of the point is constant, andn is 
greatest and the gyration slowest, at first, it follows that 
the first spiral will be the largest. As n grows less, the 
gyration becomes more rapid, hence the next curve will 
be smaller, the next, smaller yet, and so on. 
As the gyration, the inclination, and the rate, n, may 
vary indefinitely among themselves, the rate of diminu- 
tion in the diameter of the spirals will vary almost in- 
definitely. 
THE TRAVELING OF THE TOP. 
It would seem from what has been said that the trac- 
ing should be a concentric spiral, commencing at the 
outside. It will be found on trial exceedingly difficult 
to get the top to make such a path. To approximate to 
it, the surface must be a plane as nearly level as it can 
be made. The central figure in plate III represents a 
tracing on polished plate glass, laid as horizontal as 
possible with the aid of an ordinary spirit level, yet 
there was a movement to the left. I have often had 
tracings in which, although the centre of the spiral 
travels a little, all the curves were within the larger 
one, but never one where they were absolutely concen- 
tric. 
The other tracings on this, and on plate Il, show 
abundant movement. These illustrate the third law. We 
will try to show their rationale. Let figure 3 (page 155) 
represent a bird’s-eye view of our top, inclined as in 
figure 2, and in four successive positions, the pin, or 
shaft, alone being represented. 
The body of the top may, for the moment, be consid- 
ered as so transparent as to beinvisible. The arrows show 
38s 
