April 17, 191 3] 



NATURE 



>75 



GYROSTATS AND GYR0STAT1C ACTION. 1 

 T NOW suspend the gyrostat from the horizontal 

 •*■ beam by means of this chain terminating in a hook 

 (Fig. 8), which engages, as you see, in a central 

 recess of the rim attachment. The chain, you observe, 

 carries a ball-bearing race. I place the gyrostat with 

 its axis horizontal 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 pre- 

 cession the gyrostat ascends. I transfer the hook to 



Fig. 3. — Motor-gyrostat preceding on chain support. 



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 to say. If p be 

 the spin-momentum, and the top has been properly 

 started, angular momentum about the couple-axis is 



1 Discourse delivered at the Koval Institution on Friday, February 14. by 

 Prof. Andrew Gray. F.S S. The molor-gyro-tats described are the inven- 

 tion of Dr. J. G. Gray and Mr. G. B. Burnside. The gyrostatic tops and 

 combinations used in the latter part of the lecture are due to Dr. Gray. 

 Continued from p. 153. 



NO. 2 268, VOL. 91] 



being produced at rate /*u> by this turning, and this 

 is equal to the moment of the couple. The precessional 

 motion remains at the value required to give just the 

 rate of production of angular momentum correspond- 

 ing to the couple. This is the point generally missed 

 in popular explanations of 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 this 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 somer- 

 sault, and is thereafter stable. If I reverse the direc- 

 tion 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 



Fig. 9. — Motor-gyrostat mounted to demonstrate theiprinciple of the 

 gyrostatic compass. 



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 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 real period of vibration 

 about the vertical ; in the other the period is mathe- 

 matically unreal, and the gyrostat axis moves further 

 away from the vertical. No better illustration of the 

 two cases of the equation can be found. 



The behaviour of the tray-gyrostat is exemplified 

 also in the gyrostatic compass. A heavy and rapidly 

 rotating flywheel is mounted so that its axis is main- 

 tained horizontal by means of an elastic support. 

 Under these conditions the equilibrium position of the 

 flywheel under the horizontal component of the turn- 

 ing 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 experi- 

 ment 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. 



