ON A DYNAMICAL TOP. 257 



It is impossible to observe this motion successfully, without the aid of the 

 coloured disc placed near the upper end of the axis. This disc is divided into 

 sectors, and strongly coloured, so that each sector may be recognised by its colour 

 when in rapid motion. If the axis about which the top is really revolving, falls 

 within this disc, its position may be ascertained by the colour of the spot at the 

 centre of motion. If the central spot appears red, we know that the invariable 

 axis at that instant passes through the red part of the disc. 



In this way we can trace the motion of the invariable axis in the revolving 

 body, and we find that the path which it describes upon the disc may be a circle, 

 an ellipse, an hyperbola, or a straight line, according to the arrangement of the 

 instrument. 



In the case in which the invariable axis coincides at 'first with the axle of 

 the top, and returns to it after separating from it for a time, its true path is 

 a circle or an ellipse having the axle in its circumference. The true principal 

 axis is at the centre of the closed curve. It must be made to coincide with the 

 axle by adjusting the vertical screws I, m, n. 



Suppose that the colour of the centre of motion, when farthest from the 

 axle, indicated that the axis of rotation passed through the sector L, then the 

 principal axis must also lie in that sector at half the distance from the axle. 



If this principal axis be that of greatest moment of inertia, we must raise 

 the screw I in order to bring it nearer the axle A. If it be the axis of least 

 moment we must lower the screw I. 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 



VOL. i. 33 



