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, b, a, 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, II is a heavy ring 

 cast in the same piece. Six screws, with heavy heads, x, y, z, of, y', z', work 

 horizontally in the ring, and three similar screws, I, 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 o. 



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 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. 



