568 PROFESSOR MAXWELL ON A DYNAMICAL TOP. 



The smaller the difference between the moment of inertia about the axle and 

 about the mean axis, the more eccentric the ellipse will be ; and if, by screwing 

 the bob down, the axle be made the mean axis, the path of the invariable axis 

 will be no longer a closed curve, but an hyperbola, so that it will depart alto- 

 gether from the neighbourhood of the axle. When the top is in this condition 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 xx 1 the least. The major axis of the ellipse described by 

 the invariable axis will now be perpendicular to xx l , 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 practised, 

 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 gravity, 

 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 phe- 

 nomena 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 axis disturbed 



