July 25, 1918] 



NATURE 



417 



steacJ\ revolving motion, throwing a shadow moving 

 to and fro in plane vibration on the wall. 



The bicycle-wheel forms a compound pendulum, 

 with the axle held fixed, and put out of balance 

 with an iron rod between the spokes ; and then the 

 v^heel can show off oscillation of any finite extent, 

 beating the elliptic function, or it can make complete 

 revolutions, say from I to XI, or all round the clock. 



For this experiment an ordinan,- bicycle complete 

 will serve, laid on its back, using the front wheel, 

 and then the hind wheel, to show- off the effect of 

 the inertia of the chain and crank-axle. The writhing 

 of the frame on a smooth floor will illustrate the 

 stress of reaction of the frame to the motion. 



Prof. Perry has written a popular book on the 

 "Spinning Top" in his most stimulating kindergarten 

 style, but it is doubtful if he has ever seen a top of 

 the size of these bicycle-wheels ; and I wonder if he 

 has ever seen this gyroscope apparatus, although I 

 made him a present of one many years ago. 



As in skating over thin ice the novice can progress 

 swiftly, never stopping to look down at the black 

 water underneath, whereas if he paused to consider 

 the depth below he would break through and go 

 down ; so in the theory of the top the analytical diffi- 

 culties would drown the beginner if not kept out of 

 sight as long as possible. 



The kindergarten explanation of the spinning-top 

 is eloquent in answer to the beginner's question of 

 the how and why. But in mathematical treatment it 

 is the '"how much?" That is the question. 



Crabtree's " Gyroscopic Motion " goes more deeply into 

 the mathema'tics of the subject in elegant treatment; 

 and here is a Report on Gyroscopic Theory (19 14) 

 intended to serve for reference on the complete theory, 

 where no analytical difficulty is avoided when anv 

 practical problem arises for solution. And the simple 

 apparatus shown here is intended to be applied at 

 once to a practical test of any ne\<- suggestion of 

 harnessing a top or gyroscope. 



Attention was directed to the deformable Henrici 

 hyperboloid passing through the shape of a con focal 

 system. This was employed by Darboux for the 

 material representation of a state of top-motion by 

 geometHcal constants. Calculation was thereby re- 

 placed by measurement on a drawing. 



Then there is Kirchhoff's kinetic analogue of the 

 bent and twisted w-ire, to associate in making a mental 

 picture of the top-motion in all its complexity. 



This analogue states that if an elastic round wire, 

 rod, or shaft is bent and twisted into its most general 

 tortuous curve under the action of an equal opposing 

 wrench at each end, the shape of the curve is such 

 that if a ooint moves along the curve with constant 

 velocity, the hodograoh of its motion is a spherical 

 curve, which can be identified as the curve described 

 by a point fixed in the axle of a s\mmetrical top 

 spinning about a fixed point, as in this small cup, 

 and in the same period by a proper choice of the con- 

 stant velocity. 



In most practical applications the nutation is small 

 and imperceptible, though never absent entirely, and 

 the motion is apparentlv steady, with the axle at a 

 constant inclination and. moving round with uniform 

 precession ; in the KirchhofT analogue the shaft is 

 sprung slightly. 



The curious property of a spinning bodv in rising 

 erect in opposition to gravity, or of running along 

 like a hoop or bicyde without falling over, has directed 

 attention to the distinction between balance and 

 stability according as it is statical or dynamical. 



It was mentioned that Lord Kelvin, just twentv- 

 five years ago. lectured at the Royal Institution on 

 '* Isoperimetrical Problems — Dido, or Making Things 

 Spin," on a sheet of plate-glass fenced with a frame. 

 NO. 2543, VOL. lOl] 



Since Newton compared himself with a child gather-" 

 ing pebbles on the shore, he set the fashion for his 

 rivals of 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 readins; brings not 

 A spirit and a judgment euual 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 inioxicate, c-ollectiqg toys 

 And trifles for choice matters, worth a sponge, 

 As cniklren gathering pebbles on the shore. 



In the contrast of balance, statical and dynamical, 

 the C.G. in statical equilibrium seeks the lowest posi- 

 tion 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 high up 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 misappre- 

 hension of theory, as of lowering the soldier's knap- 

 sack, or ballasting a ship too low and so making it 

 uneasy among waves, as recommended by Euler ; 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 over 

 the wheels, as high as it can go under the old cratnp- 

 ing limitation of the loading gauge of our bridges and 

 tunnels. 



A literary friend has directed attention to De 

 Quincev's account of a wonderful brother, who 

 claimed the power of rising against gravity to walk 

 like a fly on the ceiling, provided with spin enough, 

 but that he would require the flagellation of a whip- 

 top in harness, emblem of fortitude in adversity. 



Tu ne cede malis, sed contra audentior ito. 



Without attaining so far as the positive levity of 

 De Quincey's brother, we have seen how a top can 

 be made to climb a pole in the model described to 

 the Royal Society by Mr. Tournay Hinde in their 

 Proceedings. And Brennan can make it run along 

 the tight-rope or on a single rail, concealed in 

 harness inside a carriage, to which it gives the up- 

 right stability, acting automatically as the brain in 

 riding a bicycle. 



In the description of the American poet — 



Are you the Mr. Brendan makes gyroscopic tops v 



To keep a car in balance when It runs, or if i' stop«, 



On single rail or wire rope that's «tretched across a chasm ': 



Pray write and tell me, Mr. I'rennan, if you're the man that has cm. 



Axial Stability of motion of an elongated body 

 through the air, an arrow, bullet, or shell, is main- 

 tained by the gyroscopic action of the spin imparted 

 by the rifling, and the calculation of the least amount 

 required is a delicate question of dynamics. No more 

 spin should be given than absolutely necessary, or the 

 shell or bullet will be uneasy in flight, as a ship is 

 uneasy among waves if bottom-heavy, as recom- 

 mended by Euler, the weights stowed too low. 



Passing from small to large applications, the 

 Parsons turbine in the steamship requires to be 

 treated on gyroscopic theory for motion among waves. 

 Rolling does not affect them, but the internal stress 

 due to pitching becomes important, and must receive 

 investigation. 



So, too, if electric dynamos are mounted with axle 

 across the ship, they are very sensitive to the rolling. 



