﻿Pseudo- Regular Precession. 185 



Or the position of M is determined by drawing QQ' 

 parallel to OC, to cut the circle on the diameter OC in 

 Q,Q', when MQ 2 = ±Z: 2 cos0. 



This is for the small value of /-t in fig. 3, and the quiet 

 precession when M is taken close to C, the other point Q' 

 will determine a motion where the precession //, is swift and 

 the motion violent. 



Fig. 3. 



OC, = 20M. 



MK' = 2MK. 



e 



Spinning upright with cos 0=1, fi-\ = -^ R ; and the 



fx A. 



two values of fi will give the independent normal invisible 



n 2 

 circling of the axle round the vertical ; there will be ___ 



rapid beats for one slow beat of the axle. P 



The general slight oscillation will be compounded of these 



two circlings, adding up to an epicyclic motion of the axle, 



a result obtained in this manner without any appeal to 



approximation. 



In fig. 2, the axle is pointing downward at *an angle 6 



with the nadir ; here the slow precession of K is retrograde, 



but in the swift violent motion of the associated K', the 



precession is direct. 



