ON A DYNAMICAL TOP. 259 



it must be spun gently, for it is very difficult to manage it when its motion 

 gets more and more eccentric. 



When the bob is screwed still farther down, the axle becomes the axis of 

 greatest inertia, and xtf the least. The major axis of the ellipse described by 

 the invariable axis will now be perpendicular to axe 1 , and the farther the bob 

 is screwed down, the eccentricity of the ellipse will diminish, and the velocity 

 with which it is described will increase. 



I have now described all the phenomena presented by a body revolving freely 

 on its centre of gravity. If we wish to trace the motion of the invariable axis 

 by means of the coloured sectors, we must make its motion very slow compared 

 with that of the top. It is necessary, therefore, to make the moments of inertia 

 about the principal axes very nearly equal, and in this case a very small change 

 in the position of any part of the top will greatly derange the position of the 

 principal axis. So that when the top is well adjusted, a single turn of one of 

 the screws of the ring is sufficient to make the axle no longer a principal axis, 

 and to set the true axis at a considerable inclination to the axle of the top. 



All the adjustments must therefore be most carefully arranged, or we may 

 have the whole apparatus deranged by some eccentricity of spinning. The method 

 of making the principal axis coincide with the axle must be studied and prac- 

 tised, or the first attempt at spinning rapidly may end in the destruction of 

 the top, if not of the table on which it is spun. 



On the Earth's Motion. 



We must remember that these motions of a body about its centre of gra- 

 vity, are not illustrations of the theory of the precession of the Equinoxes. 

 Precession can be illustrated by the apparatus, but we must arrange it so that 

 the force of gravity acts the part of the attraction of the sun and moon in 

 producing a force tending to alter the axis of rotation. This is easily done by 

 bringing the centre of gravity of the whole a little below the point on which 

 it spins. The theory of such motions is far more easily comprehended than 

 that which we have been investigating. 



But the earth is a body whose principal axes are unequal, and from the 

 phenomena of precession we can determine the ratio of the polar and equatorial 

 axes of the "central ellipsoid;" and supposing the earth to have been set in 

 motion about any axis except the principal axis, or to have had its original 



332 



