640 Professor Andrew Gray [Feb. 14, 



and leave it to itself. The centre 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 preces- 

 sion 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 direction. 

 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 towards an instantaneous position of the couple axis at right 

 angles to it, at angular speed w say. If /x be the spin-momentum, and 

 the top has been properly started, angular momentum «^om^ the couple- 

 axis is being produced at rate jxw 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. 



It 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 tliis wooden tray (Fig. 9). The 

 pivots carried by the rim of the gyrostat engage on bearings provided 

 in the tray, and these are on a level with the centre 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 re- 

 mains again (piiescent. 



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 t;s to render the two directions coincident. It appears 

 as if the arrangement 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 



