Hotatory Motion, the Gyroscope, ^-c. 135 



produce rotation about a different axis is continuous. As the weight is 

 fixed on the spindle of the gyroscope, the axes about which it is in suc- 

 cession tending to produce rotation are horizontal, and at right angles 

 to the spindle. The obvious result of the continued action of the second 

 force will be to cause the position of the actual axis of rotation to be 

 continually varying. Airy demonstrates that if a uniform force act con- 

 tinuously upon the body, tending to give it a motion of rotation about 

 an axis which is always at right angles to the axis about which it is at 

 each instant revolving, and always in the same plane, the angular velo- 

 city of the body will be unaltered ; and the position of the axis of rota- 

 tion will have a uniform angular motion in space. In the case of the 

 earth, the action tending to turn it about the intersection of the equator 

 with the ecliptic, is constantly being, as it were, ti'ansferred from those 

 pai'ts of the equator which are approaching the ecliptic to those which 

 are receding from it. This is the same as though in the sphere repre- 

 sented in figs. 1 and 2, the second force which commenced acting 

 downwards on the point a, were being continually transferred to the 

 points c, &c., forming the poles of the successive new axes. We have 

 not, however, yet made out that the original axis a would move to c ; 

 did it do so, we should at once have the case to which Airy's demonstra- 

 tion last referred to applies, by attaching the weight to the point A ; 

 but in the case of the perfect sphere the point a descends. In con- 

 sidering what will be the action of a perfect rotating sphere, supported 

 at its centre, but free to rotate about any diametrical axis, with a weight 

 attached to one of the poles of its original axis of rotation, let the 

 original axis be horizontal, and let it be projected, or pierce the surface 

 of the sphere in the point a, fig. 3, the weight being attached to this point. 

 Were the sphere not rotating, the weight would turn it about the axis 

 through h, and would descend in the direction of the arrow d, and rise 

 up on the other side of the sphere, until it attained its original height, 

 provided, of course, no resistance were encountered. The weight would 

 then return, and it would continue to oscillate backwards and forwards, 

 like a pendulum. If, however, the sphere rotates very slowly about the 

 axis a, say in the direction of the arrow e, then the effect of the applica- 

 tion of the weight will be to make the sphere turn about a horizontal axis 

 between a and b, and very near the latter. For the instant, this new 

 axis is precisely as though its poles turned in fixed bearings, and the 

 weight turns with the sphere about it, and for the instant moves in a 

 plane at right angles to it, and consequently in an arc of a less radius 

 than that of the sphere. An oscillation of the weight about this new 

 axis would not bring it up on the otlier side of the sphere to a point 

 directly opposite to its original point, but to one nearer to the point b. 



