191^^] on Gyrostats and Gyrostatic Action 639 



which as jou 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 freedom 

 to fall over towards you, or towards 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 stabilise two non-rotational instabihties, but not one. In 

 point of fact, a system possessing non-rotational freedoms, all of 

 which are unstable, can be stabilised if the number of freedoms is 

 even, but not if the number 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 shghtly. 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 gyrostat tending to turn its axis in a horizontal plane. 

 In consequence the gyrostat tilts over on the bar — in other words, it 

 has a precessional 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 hori- 

 zontal motion is opposed and reversed, and with the reversal the 

 gyi'ostat 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 



