GYROSTATS AND GYROSTATIC ACTION—GRAY. 203 
in the tray, and these are on a level with the center of gravity of the 
whole. I hold the tray so that its plane is horizontal, and carry it 
round in a horizontal circle. Nothing happens. Still holding the 
tray so that its plane is horizontal, I carry it round in a horizontal 
circle in the reverse direction. The gyrostat immediately turns a 
somersault and is thereafter stable. If I reverse the direction of 
rotation of the tray, again the gyrostat turns a somersault and 
remains again quiescent. 
The gyrostat is stable, with its axis vertical, so long as the direction 
of spin coincides with that in which the tray is being turned. If 
this latter direction is reversed, the gyrostat turns a somersault so as 
to render the two directions coincident. It appears as if the arrange- 
ment had a will of its own, and refused to be carried round against its 
direction of spin. 
The theory of this experiment is very instructive. Both cases are 
represented by one differential equation, but in one case there is a 
real period of vibration about the vertical; in the other the period 
is mathematically unreal, and the gyrostat axis moves farther away 
from the vertical. No better illustration of the two cases of the 
equation can be found. . 
The behavior of the tray gyrostat is exemplified also in the gyro- 
static compass. A heavy and rapidly rotating flywheel is mounted 
so that its axis is maintained horizontally by means of an elastic sup- 
port. Under these conditions the equilibrium position of the flywheel 
under the horizontal component of the turning velocity of the earth 
(which corresponds to the turning of the tray) is arranged to be that 
in which the axis of rotation points due north and south. If time 
permitted, I should be glad to make an experiment with a carefully 
balanced motor gyrostat, which would not only show the turning of 
the earth under the gyrostat, but enable the rate of turning to be 
measured. 
I would now direct your attention to this motor gyrostat, which 
forms the bob of an ordinary compound pendulum. (Fig. 10.) The 
tube carrying the gyrostat is attached, by means of a universal joint, 
to the apex of a triangular stand, made of telescope tubing. The 
gyrostat is attached to the lower end of its supporting tube, by 
means of a special cap provided with spring contact pieces, to allow 
the current to be led into the motor, and the flywheel is free to 
rotate about an axis coincident with the rod. Screwed to the lower 
side of the gyrostat is a pen, which presses lightly on a card placed 
below. 
We have now the pendulum rod in the vertical position. I draw 
the pendulum to one side and let go, when you see that it vibrates to 
and fro, and the pen traces out a straight line on the paper. The 
flywheel has as yet no spin. I start the flywheel revolving, draw 
