GYROSTATS AND GYROSTATIC ACTION—GRAY. 197 
in'point of fact, and this is the secret of the whole affair, this turning 
of the body as a whole amounts to the production of spm momentum 
about the couple axis at exactly the proper rate. It is quite easy to 
prove this by the consideration, in the most elementary way, of the 
accelerations of the different particles composing the wheel. 
The turning of the spin axis toward the couple axis is called a 
precessional motion, from a similar motion of the earth which pro- 
duces the astronomical phenomenon called the precession of the 
equinoxes. The turning action, or couple, as I shall now call it, may 
be said to cause the flywheel to ‘‘precess”’ toward the couple axis. 
This relation of directions is very important, and should be kept 
always in mind. 
If this turning response of the body, about an axis which we shall 
call 3, is prevented when turning about an axis 2, at right angles to 
3, is changing the direction of the axis of a rotor—an axis 1, say, at 
right angles to 2 and 3—a preventing couple, usually called gyro- 
static, about the axis 3, must be applied by the bearings to the axle 
of the rotor, and therefore an equal and opposite couple by the axle 
to the bearings. This couple, it is easy to prove, is equal to the 
product of the spin momentum and the angular speed at which the 
direction of the axis of the rotor is being changed. Thus the greater 
the moment of inertia of the rotor, or its angular speed, or the angular 
speed of the change of direction of the axis, the greater is the gyro- 
static couple. 
For example, the rotor of a dynamo, mounted on one of the decks 
with its rotor axis athwartship, applies, when the ship rolls, a couple 
to the bearings, the plane of which is parallel to the deck, and which 
consists of a forward force on one bearing and a sternward force on 
the other. These forces are reversed with reversal of the direction 
of rolling, so that an alternating force is applied to each bearing 
tending to shear it off the deck. Thus if the bearings are at all 
loose, the axle will knock alternately on the front and back of each 
bearing. 
Similarly the axle of the rotor of a fore-and-aft turbine, when the 
ship pitches, applies a force to port to the bearing at one end, and a 
force to starboard at the other end, which forces are reversed when 
the direction of the pitchmg motion is reversed. When the course 
is being changed the forces of the gyrostatic couple are applied to 
the top of one bearing and the bottom of the other. 
Now, returning to the pillar gyrostat, and putting the flywheel 
in rapid rotation, [ turn the pillar round on the table. I have 
turned, as you see, the base round through one revolution, and 
throughout the turning motion the axle of the flywheel has remained 
pointing in the same direction. The friction at the axle about 
which I have turned the pillar, which, you will remember, was suffi- 
