Rotatory Motion, the Gyroscope, 4'c. 133 



fall, but moves horizontally round the pillar, its own weight acting just 

 like the added weiglit in the Bohnenberger apparatus. 



In proceeding to explain these phenomena, it will simplify matters if 

 we, in the first instance, confine our ideas to the case in which the 

 spindle of either instrument is in a horizontal position at the com- 

 mencement of the experiment, and the force of gravity is acting in such 

 a way as would bring the spindle down into a vertical position, were the 

 fly-wheel not spinning. And first — the fact that the instrument is sup- 

 ported at a point, and that any movement in it must be one of rotation 

 or oscillation about an axis passing through that point, must be care- 

 fully kept in view. Thus the fly-wheel spins about one horizontal axis, 

 and gravity tends to make it turn about another horizontal axis, these 

 two axes passing through this point of support, and being at right 

 angles to each other. 



It will very much facilitate our conception of the various circum- 

 stances and conditions under investigation, if we consider the rotatin 

 body as forming part of a sphere of which the centre is the point of 

 support of the body. And, first, let us consider the action on an entire 

 sphere, of two equal impulses, tending to turn it about separate hori- 

 zontal axes at right angles to each other, the sphere being supposed to 

 be supported at its centre, but free to turn about any diametrical axis 

 whatever. Such a sphere is represented in figs. 1 and 2, fig. 1 being 

 an elevation, and fig. 2 a corresponding plan. Let one impulse tend to 

 turn the sphere about the axis A, the full lines being the paths various 

 points on the surface of the sphere would pursue round this axis, and 

 the arrow-heads indicating the direction of the motion. Let the other 

 impulse tend to turn the sphere about the axis b, the dotted lines being 

 the paths of various points round this axis, and the corresponding arrow- 

 heads showing the direction of the motion. Whatever impulses may 

 have acted on a sphere, it cannot, when left to itself, rotate about more 

 than one axis at a time ; for each particle continues to move in one plane 

 as long as no deflecting force is applied to it ; and on account of the 

 rigidity of the body, the planes of motion of all the particles must be 

 parallel to each other, and at right angles to the axis. Hence in the 

 case under considei*ation, the two impulses must combine to produce a 

 rotation about some single diametrical axis, and it makes no difference 

 whether the impulses are imparted simultaneously or in succession. We 

 have therefore to determine the resultant axis, and it must obviously 

 lie between the two axes a, b, and also in the same plane with them, — 

 for no reason can be suggested why it should be to one side of that 

 plane, rather than to the other. And accordingly we find that a point, 

 c, midway between the poles a, h, of the two axes, and at the part where 



