288 Sir George Greenhill [May 3, 



Thus the top in harness is like the Irish pig, in Professor Perry's 

 simile, who cannot be persuaded to accompany his master to market 

 except by steerino^ him sideways into the ditch, a veritable tour-de- 

 force — "transferring forces round the corner," in the title of the 

 pamphlet on the Sperry Gyro-Compass. This sidelong force makes 

 its appearance in the electrodynamical equations, and is called the 

 gyroscopic term in consequence. 



The wooden ball on this wheel was fitted originally as a protec- 

 tion for the head underneath when the wheel was suspended from 

 the ceiling. The ball comes in useful here as showing the influence 

 of the rounding of the point of a top in enabling the top to rise, 

 when free to wander about the floor, and not constrained in this small 

 cup. It is the friction of the ball-point causes the top to rise, but 

 ultimately kills out the rotation. 



We try to avoid in these experiments the hideous unreality of 

 perfectly rough and perfectly smooth, in the school-book jargon, by 

 spinning the top either in the small cup or else on the rounded point 

 on the floor. The wheel comes to rest when the rim reaches the 

 floor, and to study the motion when the axle makes a greater angle 

 with the zenith, and moves about in the neighbourhood of the nadir, 

 we turn to this other apparatus, an ordinary 2«-inch bicycle wheel — 

 the axle screwed into a steel stalk — a short length of rifle barrel, 

 suspended from a lug on a bicycle hub, allowing motion in altitude 

 and azimuth. An ordinary hook attachment would serve as well, I 

 believe, if well oiled. The hub is fastened in this iron bracket, 

 bolted to the underside of a beam or sleeper, and this should be 

 heavy enough to absorb vibration — not a thin board, or lath, or little 

 stick as I found them trying in Rome with the present I had made 

 of the apparatus. The model is easily constructed, as the complicated 

 parts, wheel and hub, can be bought cheap, ready made. Spin the 

 wheel by hand ; and project the axle, to obtain any desired gyro- 

 scopic motion— undulating, looped, cusped. 



The analytical mathematical theory is abstruse, and requires the 

 elliptic function, in a much more complicated form than for the 

 simple pendulum in plane oscillation of finite extent. But here are 

 two simple cases of motion where the solution is quasi-algebraical, 

 and so may interest the mathematical student present : — 



I. Hold the axle out and project it horizontally, without spinning 

 the wheel, when the motion is that of a spherical pendulum, a simple 

 plummet at the end of a thread. 



II. Spin the wheel, and allow the axle to fall from rest at a cusp 

 at an upward angle so that the axle reaches the horizontal in its 

 lowest position, rises again, and so continues. 



The exact interpretation is rather delicate of the rotation of the 

 wheel about a moving axle. Thus, although we start with the wheel 

 at rest on the axle, we cannot turn it by twirling the axle. But 

 moving the axle round in a conical way to rest again, we find that 



