290 Sir George Greenhill [May 3, 



toy of Archytas — a New Year's gift I had made to Mrs. Maxwell — 

 and giving iis a witty lecture all the time. 



Another piece of advice is, " Never grasp the wheel except at the 

 axle," or it will fly at you. But this advice was a direct challenge to 

 the young original researcher. I had turned my back for a moment, 

 and heard a musical sound as if a bell had been struck. There was 

 young Research, rubbing his head. Luckily no serious harm was 

 done, and we gave him the consolation : " It proves you are not 

 cracked." 



Poincare was so rash as to declare the problem of three bodies a 

 .great difficulty, much more difficult than even he imagined. Here 

 was another direct challenge to original research, to tempt him away 

 from all other interest ; as formerly, in ancient history, the lure ^vas 

 the squaring of the circle or trisection of an angle. 



The bicycle-wheel is detached by unscrewing the pin, as so can be 

 used, as well as the large wheel, to imitate the ordinary spinning-top. 

 We can also realize the experiment described in Maxwell's " Life " of 

 the " Top on the top of a top," an allusion to some forgotten toy of 

 1862. The large wheel is spun, and one holds the stalk while I spin 

 the small wheel, the same way to secure stabihty, and place it gently 

 in the cup here. Tins gives two links of a gyrostatic chain, which 

 we may imagine repeated in a chain or pile of wheels like a will-o'- 

 the-wisp, or suspended from the ceiling, as in Fig. 56 in Perry's 

 " Spinning-Tops," to serve as a mechanical model of the electro- 

 magnetic rotary polarization of light. 



Sir William Thomson gave an elaborate mathematical investiga- 

 tion, but this can be simplified and brought into elementary treatment 

 by considering the chain as a uniform helical polygon rotating 

 uniformly round the vertical, as I have explained in my Report on 

 Gyroscopic Theory. Any discussion of a double pendulum, like a 

 bell and clapper or a chain of links, is simplified in this manner by 

 comparing the oscillation with a steady revolving motion, throwing 

 a shadow moving to and fro in vibration. 



Put the wheel out of balance by this rod between the spokes, 

 and hold the axle, to make it serve as a plane pendulum, to show 

 off oscillation of any extent, or complete revolutions, without catch- 

 ing in any of the surroundings. Turn a bicycle upside down on a 

 table, and there is no need to dismount the front wheel, used as a 

 pendulum. The muscular sense of trying to hold the axle fixed will 

 give an idea of the reaction, as for instance in ringing a large bell. 

 The axle can be held at any angle : here nearly vertical, like the 

 hinge line of a door, a little out of plumb, when it is called a hori- 

 zontal pendulum, useful in the measurement of slight variation in 

 gravity, such as due to lunar or tidal influence, as in Sir George 

 Darwin's investigations. 



I am reminded of another problem to interest the mathematical 

 students I see here. Hold the axle at the slope of the edge of this 



