58 Mr Basset, On the Motion of a Ring [Jan. 31, 
Z 
Sy 
6 
O 
XG 
B ve 
The equations of momentum are 
(E cos 0+ €sin 0) cos —7 sin v= 0, 
(Ecos 8+ € sin @) sin + 7 cos fr = 0, 
- €sin6+ CcosO=F+ €, cosa; 
whence 
&=—(F+ €, cos a) sin A 
7=0 5 tices desrmo eee 
€=(F+ 6, cos a) cos @ | 
Since the components of momentum parallel to the axes of X 
and Y (which are fixed in direction, but not in position because O 
is in motion) are zero throughout the motion, the angular momen- 
tum about OZ is constant, whence 
— Aw, sin 8+ CO, cos 0 = G+ CO, cosa ...........(7). 
The equation of energy gives 
Pui+ Rw’ + A (o2 + &) = const., 
(6). 
therefore 
(F+€,cosa)’sin?@ {(f+€,cosa)cosO—€,)? | {G@+CQO (cosa—cos6)}? 
P ue R ES Asin? 0 
+ Aé’= const. = its initial value............... (8). 
This equation determines the inclination @ of the axis. 
So far our equations have been perfectly general, we shall now 
introduce the conditions of steady motion. These are 
=a) ahaa eo = = 0 eee (9), 
whence (7) becomes 
2A pe SUI OSG ais 2 ence ahie oo Haye ata (10). 
