1887.] in an Infinite LInquid. 49 
3. Let the ring be set in motion by means of an impulsive 
couple G about any diameter OB of its circular axis. 
The axis OC of the ring will evidently move in a fixed plane, 
which is perpendicular to the axis of the couple. Let @ be 
the inclination of OC to OZ at time ¢; uw, w the velocities of O 
along OA and OC. 
The principle of Conservation of Linear Momentum gives, 
—&sin@+fcos0=6,, 
Ecos @ + sin 0=0, 
whence 
Pu =—£€, sin 0 
Rw=-— €,(1 — cos @) 
If 2, # be the velocities of O along and perpendicular to OZ, 
then 
#&=ucos0+wsin 6, 
2=w cos @— usin 6. 
Therefore 
= tl pop) sin 8 cos 6 sin 8] 
Tlic ek Ra (4) 
a “ 1) 6 Beh): 
eee cos’ 6 cos 6 | 
Also 
OT = Pw + Rw? + AP + Ke = const. 
