Now let us make the axes of inertia in the plane of the ring unequal. We may do this by screwing the balance screws $x$ and $x^1$ farther from the axle without altering the centre of gravity. Let us suppose the bob $B$ screwed up so as to make the axle the axis of least inertia. Then the mean axis is parallel to $xx^1$, and the greatest is at right angles to $xx^1$ in the horizontal plane. The path of the invariable axis on the disc is no longer a circle but an ellipse, concentric with the disc, and having its major axis parallel to the mean axis $xx^1$. 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 altogether 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 $xx^1$, 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 practised, or the first attempt at spinning rapidly may end in the destruction of the top, if not the table on which it is spun. On the Earth’s Motion