292 Sir George Greenhill [May 3, 



fixed in the axle of a symmetrical top spinning about a fixed point, 

 as in this small cup, and in the same period by a proper choice of 

 the constant velocity. 



In most practical applications the nutation is small and imper- 

 ceptible, though never absent entirely, and the motion is apparently 

 steady, with the axle at a constant inclination, and moving round 

 with constant precession. In the " Kinetic Analogue " the shaft is 

 sprung slightly from the straight. 



The curious property of a spinning body in rising erect in oppo- 

 sition to gravity, or of running along like a hoop or bicycle without 

 falling over, has directed attention to the distinction between Balance 

 and Stability, according as it is Statical or Dynamical. 



I recall the lecture here of Lord Kelvin's, just twenty-five years 

 ago, Isoperimetrical Problems — " Dido, or Making things spin," on 

 a sheet of plate-glass fenced with a frame. 



Since Newton compared himself to a child gathering peljbles on 

 the shore, he set the fashion for his rivals in making them spin. 

 But Newton took it for granted his audience knew he was quoting, 

 against himself, the lines from "Paradise Regained " : — 



"Many books 

 Wise men have said are wearisome. 

 Who reads incessantly, and to his reading brings not 

 A spirit and a judgment equal or superior, 

 (And what he brings, what needs he elsewhere seek ?) 

 Uncertain and unsettled still remains, 

 Deep versed in books and shallow in himself. 

 Crude or intoxicate, collecting toys 

 And trifles for choice matters, worth a sponge. 

 As children gathering pebbles on the shore." 



Demosthenes tells us he put the pebbles in his mouth he gathered 

 on the shore, as a cure for his stammer and indistinct articulation. 



In the contrast of balance, statical and dynamical, the C. G. 

 in statical equilibrium seeks the lowest position it can find ; but it 

 rises as high as it is able in dynamical stability of balance, as of a 

 sleeping top or bicycle. A top is said to sleep when spinning steadily 

 upright ; man or an animal sleeps lying down, with the C. G. low. 

 But "for ease of progression a man assumes the noble upright attitude 

 of a biped, not on all-fours, or rides upright on the back of a horse or 

 on a bicycle. Any burden, rifle or knapsack, he carries as high as 

 possible. Mounted still higher on stilts, his progress is not more 

 difficult, with the confidence of . experience. Confusion between 

 statical and dynamical stability of balance has led to serious mistakes 

 and misapplication of theory, as of lowering the soldier's knapsack, 

 or ballasting a ship too low and so making it uneasy among the 

 waves, as recommended by Euler, a Swiss admiral, or spreading the 

 railway gauge to lower the boiler and carriage body between the rails, 

 in Brunei's idea. The modern locomotive is seen to-day high up 



