136 Mii, E. Hunt on certain Phenomena connected with 



The greater the original velocity of rotation of the sphere is, compared 

 with that which the weight tends to impart, the smaller will be the 

 semicircle or other curve tlirough which the weight wiU move, and 

 the less will be the horizontal arc on the sphere which such motion 

 will measure from the starting point a. Let the original velocity of 

 the sphere be such that in a verj' short interval of time the effect of 

 the weight is equivalent to that of an impulse, which would cause the 

 new resultant axis to be in the pointy'; then the weight will begin to 

 move like a pendulum in the circle a i, whose radius is fa. A pendulum, 

 however, notwithstanding its motion, is always exerting a pressure on 

 its point of support ; and in our case the weight, notwithstanding its 

 motion round the centre f, is constantly tending to turn the sphere 

 about a new horizontal axis. The consequence of this is, that the 

 actual axis of rotation is constantly moving towards h ; and as the weight 

 is alwavs moving in an arc, of which the pole /or h of the axis is the 

 centre, it will not describe the semicircle a i, but the curve a k. A 

 complete investigation shows that by the time the weight reaches k, the 

 pole of the actual axis of rotation will also reach that point. The 

 upward motion of the weight due to the acting energy caused by its 

 descent will then be neutralized by the retarding action of gravity, and 

 the sphere will be in the precise condition in which it was at starting, 

 except that its axis is now in k, instead of a. The action described will 

 be repeated, the axis moving to h, and the weight moving through the 

 curve projected hi k I b, precisely similar to the arc a k, the weight 

 making a series of vertical oscillations, whilst the position of the actual 

 axis of rotation travels round in the horizontal plane. 



In applying what has been said of the sphere to the case of the 

 gyroscope, we may suppose the latter to be formed out of the former, 

 by cutting portions away. Thus A, in figs. 1 and 2, being the original 

 axis of rotation, and the centre of the sphere being the point of support, 

 if we cut away all the portions but that shaded by hoi-izontal Unes in 

 figs. 1 and 2, and shown separately in figs. 4 and 5, we shall obtain a 

 sufficiently close approximation to the Bohnenberger gyroscope — sup- 

 ported at its centre. If a weight be apphed at one end of the spindle 

 A, it will tend to turn the wheel about a horizontal axis at right angles 

 to the spindle ; but this tendency combining with the motion ah-eady 

 possessed by the wheel, will make it tend to turn about an intermediate 

 axis passing through c, fig. 4, the precise position of this axis depending 

 on the ratio of the two velocities, whilst it will be the same as though 

 the sphere were complete ; for, as before mentioned, the action on each 

 particle is the same as if it were independent of the others. The same 

 weight, however, will produce a greater velocity in the gyroscope fly- 



