56 Mr Basset, On the Motion of a Ring [Jan. 31, 
the motion will be stable provided there is sufficient circulation ; 
but when there is both circulation and rotation about the axis, the 
motion is always stable. A general explanation of the reason of 
this has already been given in Art. 4.] 
6. Another kind of steady motion may be obtained by setting 
the ring in motion by means of a couple G about a diameter of its 
circular axis, and at the same time applying an impulse ¢, in the 
opposite direction to that of the cyclic motion. 
The effect of the latter impulse is to destroy the linear 
momentum of the system, hence 
E=0)  G—0: 
Therefore u=0, w=-3. 
Karchhoff’s 5th equation gives 
=const. = G= AO. 
The motion of the ring is such that its centre of inertia 0, 
describes a circle about a fixed axis parallel to the axis of the 
couple, through which the plane of the ring always passes. If r 
be the distance of O from this axis, 
a warb= 
As 
es 
In order to determine the stability, we must put in the general 
equations of motion, 
E= Pu, n = Po, C= Rw, 
r= dAo,, @=G+Ao,, v=0, 
w= 40, 0,=-Fto, 
where the quantities wu, v, &c., on the right-hand sides of these 
equations, are small quantities in the beginning of the disturbed 
motion. Also, if the axes are fixed in the ring, 
G 
6. =o,, oo tgs W,, Ge) 
and the equations of disturbed motion are 
G 
Pi + A 
w=, 
