If this principal axis be that of _greatest_ moment of inertia, we must _raise_ the screw $l$ in order to bring it nearer the axle $A$. If it be the axis of least moment we must _lower_ the screw $l$. In this way we may make the principal axis coincide with the axle. Let us suppose that the principal axis is that of greatest moment of inertia, and that we have made it coincide with the axle of the instrument. Let us also suppose that the moments of inertia about the other axes are equal, and very little less than that about the axle. Let the top be spun about the axle and then receive a disturbance which causes it to spin about some other axis. The instantaneous axis will not remain at rest either in space or in the body. In space it will describe a right cone, completing a revolution in somewhat less than the time of revolution of the top. In the body it will describe another cone of larger angle in a period which is longer as the difference of axes of the body is smaller. The invariable axis will be fixed in space, and describe a cone in the body. The relation of the different motions may be understood from the following illustration. Take a hoop and make it revolve about a stick which remains at rest and touches the inside of the hoop. The section of the stick represents the path of the instantaneous axis in space, the hoop that of the same axis in the body, and the axis of the stick the invariable axis. The point of contact represents the pole of the instantaneous axis itself, travelling many times round the stick before it gets once round the hoop. It is easy to see that the direction in which the hoop moves round the stick, so that if the top be spinning in the direction $L$, $M$, $N$, the colours will appear in the same order. By screwing the bob B up the axle, the difference of the axes of inertia may be diminished, and the time of a complete revolution of the invariable axis in the body increased. By observing the number of revolutions of the top in a complete cycle of colours of the invariable axis, we may determine the ratio of the moments of inertia. By screwing the bob up farther, we may make the axle the principal axis of _least_ moment of inertia. The motion of the instantaneous axis will then be that of the point of contact of the stick with the _outside_ of the hoop rolling on it. The order of colours will be $N$, $M$, $L$, if the top be spinning in the direction $L$, $M$, $N$, and the more the bob is screwed up, the more rapidly will the colours change, till it ceases to be possible to make the observations correctly. In calculating the dimensions of the parts of the instrument, it is necessary to provide for the exhibition of the instrument with its axle either the greatest or the least axis of inertia. The dimensions and weights of the parts of the top which I have found most suitable, are given in a note at the end of this paper.