HKB
of these lines, and the cusps of the epicycloids lie in the curve in which the instantaneous axis travels. Some of the figures produced in this way are very pleasing.
In order to illustrate the theory of rotation experimentally, we must have a body balanced on its centre of gravity, and capable of having its principal axes and moments of inertia altered in form and position within certain limits. We must be able to make the axle of the instrument the greatest, least, or mean principal axis, or to make it not a principal axis at all, and we must be able to see the position of the invariable axis of rotation at any time. There must be three adjustments to regulate the position of the centre of gravity, three for the magnitudes of the moments of inertia, and three for the directions of the principal axes, nine independent adjustments, which may be distributed as we please among the screws of the instrument.
Figure: Figure 6
The form of the body of the instrument which I have found most suitable is that of a bell (fig. 6). $C$ is a hollow cone of brass, $R$ is a heavy ring cast in the same piece. Six screws, with heavy heads, $x$, $y$, $z$, $x'$, $y'$, $z'$, work horizontally in the ring, and three similar screws, $l$, $m$, $n$, work vertically through the ring at equal intervals. $AS$ is the axle of the instrument, $SS$ is a brass screw working in the upper part of the cone $C$, and capable of being firmly clamped by means of the nut $c$. $B$ is a cylindrical brass bob, which may be screwed up or down the axis, and fixed in its place by the nut $b$.
The lower extremity of the axle is a fine steel point, finished without emery, and afterwards hardened. It runs in a little agate cup set in the top of the pillar $P$. If any emery had been embedded in the steel, the cup would soon be worn out. The upper end of the axle has also a steel point by which it may be kept steady while spinning.
When the instrument is in use, a coloured disc is attached to the upper end of the axle.
It will be seen that there are eleven adjustments, nine screws in the brass ring, the axle screwing in the cone, and the bob screwing on the axle. The advantage of the last two adjustments is, that by them large alterations can be made, which are not possible by means of the small screws.
The first thing to be done with the instrument is, to make the steel point at the end of the axle coincide with the centre of gravity of the whole. This is done roughly by screwing the axle to the right place nearly, and then balancing the instrument on its point, and screwing the bob and the horizontal screws till the instrument will remain balanced in any position in which it is placed.
When this adjustment is carefully made, the rotation of the top has no tendency to shake the steel point in the agate cup, however irregular the motion may appear to be.
The next thing to be done, is to make one of the principal axes of the central ellipsoid coincide with the axle of the top.
To effect this, we must begin by spinning the top gently about its axle, steadying the upper part with the finger at first. If the axle is already a principal axis the top will continue to revolve about its axle when the finger is removed. If it is not, we observe that the top begins to spin about some other axis, and the axle moves away from the centre of motion and then back to it again, and so on, alternately widening its circles and contracting them.