34 Me. E. Hunt on certain Phenomena connected tvitk 



the motion about the axis a tends to lift it, whilst that about the axis B 

 tends to depress it, will be equally acted on in opposite directions, the 

 impulses being equal, and will consequently remain stationary. The 

 same will be the case, under the same circumstances, with all the points 

 lying in the line passing through the point c and the centre of the 

 sphere ; and this line being stationary, will constitute the axis about 

 which the sphere will turn, in consequence of the combined action of the 

 two impulses, provided the action on other points does not tend to make 

 any other line the axis. Airy's demonstration, however, as applied to 

 the present case, shows that the combined action on any other point 

 whatever of the sphere is such as to give it a motion round the diame- 

 trical axis passing through the point c. I need not give this demon- 

 stration here, but may state that it holds good, whether the several 

 points of the sphere are considered to be rigidly connected, or indepen- 

 dent of each other, provided, in the latter case, each point be supposed 

 to be acted on by two impulses, tending separately to produce for all 

 points the like angular velocities about the axes a and b. The ratio of 

 the angles which the axis through the point c makes with the axes a 

 and B, depends on the ratio between the angular velocities corresponding 

 to the two impulses. As before mentioned. Airy demonstrates that 

 the sines of the angles are inversely as the two separate velocities. 



If any point not in the axis through c is considered, it will be found that 

 the rotation round c is in the direction of the arrow outside the sphere 

 in fig. 1. Thus, if the sphei'e has been rotating by the first impulse 

 round the axis A, and if the second impulse is applied downwards, at the 

 point A, tending to make the sphere rotate about the axis b, the point 

 A will obviously descend, and begin to rotate in the circle a b d, about 

 the axis through c. In the case of the gyroscope, however, the end of 

 the fly-wheel spindle, which corresponds to the point A, and to which 

 the weight corresponding to a certain extent to the second impulse is 

 applied, does not descend. In other words, if a rotating sphere is acted 

 upon by an impulse which causes it to rotate on a new axis, the force of 

 the impulse will be absorbed or spent — that is, whilst it is accounted 

 for by the modified condition of the sphere, it will be incapable of pro- 

 ducing a second impulsive eflect. In the gyroscope, however, although 

 the weight appears to be constantly producing (or more correctly occa- 

 sioning) an angular motion of the spindle, its force is not spent in any 

 way, and it continues to possess as much potential energy as though it 

 were supported by a fixed point. It is this that constitutes what is 

 paradoxical in the gyroscope phenomena. 



The original rotation of the gyroscope is such as would be produced 

 b}' a single impulse ; the pressure of the weight, however, tending to 



