PROFESSOR MAXWELL ON A DYNAMICAL TOP. 567 



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 repre- 

 sents 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 instantaneous axis travels round the hoop, is in this case the same as 

 that 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. 



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 with- 

 out 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 . 



VOL. XXI. PART IV. 7 



