1918] on The Spinning-Top in Harness 2^9 



the wheel can be turned round on the axle, to an extent proportional 

 to the conical angle. And so we answer the challenge of Aristotle, 

 to turn a sphere round that is perfectly smooth, or spitted on a 

 perfectly smooth axle along a diameter. Anyone can show this off 

 with a pencil held between the finger and thumb. 



The angles employed by Euler in 1750, and denoted by 0, \b, <^, 

 are still in use in modern analysis. 



For altitude or nutation. 



x^r For azimuth or precession, clamping th-e wheel with the 

 thumb. 



</) For rubbing displacement and velocity of the wheel over 

 the axle, when undamped, whether at rest or in move- 

 ment, the axle havinu- alt-azimuth suspension. 



There is much discussion to-day of automatic gyroscopic steering 

 control, as of a flying-machine, or a torpedo under water. Any 

 suggestion can be tested here on these simple appliances, with ease 

 and immediately, of harnessing the top for useful work. Thus, I 

 hold up the wheel with the tip of a finger, and feel the pressure 

 is the same as if the wheel was at rest. There is no gyroscopic action. 

 But let go the axle and the gyroscopic effect is strong, especially if we 

 attempt to hold this vertical spindle, so as to keep the wheel 

 swinging in a vertical plane as an ordinary pendulum. A violent 

 twisting is felt, one way and the other. The same effects can be 

 shown off with this large wheel, in free precession when the ball- 

 point is resting on the hand, and then gripped. 



" Hurry the precession and the top rises, against gravity," is the 

 Kelvin rule, and we see it here. It is the secret process in plate and 

 platter-spinning. We employ the rule instinctively on the bicycle. 

 To recover the upward position we steer into a smaller circle, and the 

 machine rises ; and this operation goes on incessantly. A. bicycle 

 cannot run straight. So also we can hurry the nutation here and 

 examine the influence on the precession. Beating the large wheel 

 with a stick scarcely makes it flinch. 



The precession in this apparatus can be hurried still more by 

 projecting the wheel the reverse way, and we notice how violent the 

 motion becomes : a hint to the inventor. It is well not to show this 

 off too soon to the active mind, as it will take no further interest in 

 the former gentle motion, and will not rest till it has smashed 

 something. 



Aristotle discusses the psychology of the child's rattle, invented 

 by Archytas, in gratifying the sense of hearing something smash— to 

 come down crash on this polished floor with a top ; not so large as 

 this, though. The other invention of Archytas, of the toy flying- 

 bird, has developed in our time into a formidable engine of war. 

 But I can still picture Maxwell, in his drawing-room, chasing such a 



