268 



VII. DYNAMICS OF ROTATING BODIES. 



Now the area described in one revolution about the instantaneous 

 axis would be, if p were constant [see 55)], 



and the number of turns the body makes for one revolution of the 

 invariable axis about the X-axis is the area 57) divided by this, or 



59) 



BC 



-B)(A-C) 



This may be made as large as we please by making A approach I> 

 or C. If B = C or the ellipsoid of inertia is of revolution, about 

 the X-axis, p is constant, and the invariable cone is circular, and 

 described with uniform velocity, the number of revolutions of the 



body for one circuit of the invariable axis being /^_^\ m The motion 



is direct or inverse, 

 according as the 

 X-axis is that of 

 greatest or least 

 inertia. 



These properties 

 may all be illustra- 

 ted experimentally 

 by means of Max- 

 well's Dynamical 

 Top 1 ), constructed 

 by Maxwell for the 

 purpose of studying 

 the motion of the 

 earth about its 

 center of mass. An 

 example of this top 

 constructed in the 

 workshop of the 

 Department of Phy- 

 sics of Clark Uni- 

 versity is shown in 

 Fig. 82. The six 

 weights projecting 

 from the bell allow 



Tig. 82. . 



the moments of in- 

 ertia to be changed 

 in a great variety of ways, while at the same time the center of 



1) Maxwell, Papers, Vol. I, p. 248. 



