GYROSTATS AND GYROSTATIC ACTION—GRAY. 201 
as rigidly attached. The other stilt is simply a bit of wire pointed 
at both ends; one end rests on a table, the other, the upper end, 
rests loosely in a hollow in the upper side of this projecting piece 
attached to the case. The gyrostat is thus supported between two 
stilts, one fixed, the other quite loose, and its axis is at right angles to 
the plane of these when the arrangement stands upright. It would 
be hard to devise a more unstable support. You see that there is no 
possibility of making the arrangement stand up without spin. But 
you see, on the other hand, that there is a fair amount of stability 
with the flywheel spinning if the arrangement is allowed to oscillate, 
or, as one might say, wriggle backward and forward, horizontally. 
In the next experiment (due originally, | have been told, to the 
late Prof. Blackburn) the gyrostat is rigidly clamped to this metal bar, 
which, as you see, is hung by two chains attached to its ends. (See 
fig. 7.) The chains have been crossed by passing one through a large 
ring in the middle of the other. I turn the gyrostat so that the chains 
and the rim of the case are in the vertical plane. You observe that 
the arrangement is one of instability. The gyrostat has perfect free- 
dom to fall over toward you or toward me. Further, in consequence 
of the crossing of the chains the gyrostat is unstable as regards motion 
about a vertical axis. The arrangement is thus doubly unstable 
without rotation. 
I now set the flywheel into rapid rotation, arrange the instrument 
as before, and leave it to itself, when, as you observe, it balances with 
great ease. 
I now repeat the experiment with the chains uncrossed. Here 
there is only one instability without rotation, and the gyrostat falls 
over. An important point to be observed is that the rotation will 
stabilize two nonrotational instabilities, but not one. In point of 
fact, a system possessing nonrotational freedoms, all of which are un- 
stable, can be stabilized if the number of Se is even, but not 
if the iianbons is odd. 
A general explanation of the experiment just performed may be 
given as follows: Starting with the bar, gyrostat rim, and chains 
(crossed) in one vertical plane, we may suppose the gyrostat to fall 
over slightly. In consequence of the tilting couple introduced the 
gyrostat precesses so that its axis turns in a plane which is nearly 
horizontal. The chains now get slightly out of the vertical, and at 
once a couple hurrying the precessional motion is brought to bear on 
the gyrostat, which, in consequence, erects itself into the vertical 
position. The couple does not retard, but hurries the precession 
because the bars are crossed. This holds for both directions in which 
it is possible for the gyrostat to fall over. Again, suppose starting 
with the rim, bar, and chain in the same vertical plane, the chains 
get out of the vertical. There is now a couple brought to bear on the 
