202 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1914. 
eyrostat tending to turn its axis in a horizontal plane. In conse- 
quence the gyrostat tilts over on the bar—in other words, it has a pre- 
cessional motion about a horizontal axis in the plane of the flywheel. 
This brings into action a couple due to gravity, which is such as to 
hurry the last-mentioned precessional motion; the horizontal motion 
is opposed and reversed, and with the reversal the gyrostat regains 
the upright position. This holds for both directions in which the 
- bar tends to turn in consequence of the crossed chains. The result 
is complete stability. 
Similar explanations are applicable to the other cases of motion 
you have seen. 
I now suspend the gyrostat from the horizontal beam by means 
of this chain terminating in a hook (fig. 8), which engages in a central 
recess of the rim attachment. The chain carries a ball-bearing race. 
I place the gyrostat with its axis horizontal and leave it to itself. The 
center of gravity of the gyrostat lies vertically below the hook, and 
under those conditions there is no couple tending to tilt the instrument. 
I transfer the hook to one of the side recesses, set the gyrostat so 
that its axis is horizontal, and leave it to itself, when, instead of falling 
down, it turns its axis in a plane which is nearly horizontal. If I delay 
the precessional motion the gyrostat descends; if I accelerate the 
precession the gyrostat ascends. I transfer the hook to the opposite 
side recess, place the gyrostat so that its axis is horizontal, and again 
let go. The gyrostat precesses as before, but in the opposite direc- 
tion. Again I hurry the precession, and again the gyrostat rises; 
again I delay the motion, and the gyrostat descends. 
In these experiments, when the hook engages in either of the side 
recesses there is a couple due to gravity tending to produce angular 
momentum in a vertical plane. The axis of spin momentum turns 
toward an instantaneous position of the couple axis at right angles to 
it, at angular speed, w, say. If ” be the spin momentum, and the 
top has been properly started, angular momentum about the couple 
axis is being produced at rate yw by this turning, and this is equal to 
the moment of the couple. The precessional moment remains at 
the value required to give just the rate of production of angular 
momentum corresponding to the couple. ¢ This is the point generally 
missed in popular explanations of the gyrostatic action. 
[t is important to notice, however, that, as these experiments are 
usually carried out, the precession, though apparently steady to the 
eye, is not, strictly speaking, perfectly steady. There is a very slight 
alternate rise and fall of the axis. ‘To get quite steady motion, the 
top must not be simply spun and then left to itself; it must be 
started with the right amount of precession. 
I now place the gyrostat within this wooden tray. (Fig. 9.) The 
pivots carried by the rim of the gyrostat engage on bearings provided 
