PROFESSOR MAXWELL ON A DYNAMICAL TOP. 565 
* The instantaneous axis is not so easily observed. It revolves round the in- 
variable axis in the same time with the axis of #, at a distance which is very 
small in the case when a, d, ¢, are nearly equal. From its rapid angular motion 
in space, and its near coincidence with the invariable axis, there is no advantage 
in studying its motion in the top. 
* By making the moments of inertia very unequal, and in definite proportion 
to each other, and by drawing a few strong lines as diameters of the disc, the 
combination of motions will produce an appearance of epicycloids, which are the 
result of the continued intersection of the successive positions 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 prin- 
cipal axes, nine independent adjustments, which may be distributed as we please 
among the screws of the instrument. 
The form of the body of the instrument which I have found most suitable is 
that of a bell, (Plate XVI. fig. 6.) C is a hollow cone of brass, Ris a heavy ring 
cast in the same piece. Six screws, with heavy heads, 2, y, z, 2’, y, 2, work 
horizontally in the ring, and three similar screws, /, 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 d. 
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. Ifany 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 ad- 
vantage of the last two adjustments is, that by them large alterations can be 
made, which are not possible by means of the small screws. 
