34 2 Rotation of a Solid Body round a Fixed Point. 



the axis of moments about the axis of x, and T r the time of a re- 

 volution of the body round the axis of x, the following relation 

 between these two periods may be readily deduced from (15) : 



be 



r ' r V.( (*-*) (-*)' 



If the axis of moments, and consequently the axis of revolution, 

 be situated near the axis of greatest or least inertia, it will 

 always continue near this axis ; if, however, it be situated near 

 the mean axis, the movement of the body will be determined by 

 the following construction : Let the two cyclic planes of the 

 ellipsoid be drawn through the mean axis*; they will divide the 

 ellipsoid into two regions, in one of which is situated the axis of 

 maximum inertia, and in the other the axis of minimum inertia. 

 The spherical conic described by the axis of principal moments 

 will have the first or second of these axes for its internal axis, 

 according as R is greater or less than the mean axis. If the 

 axis of principal moments lie in one of the cyclic planes, the 

 spherical conic becomes a circle, and its two projections become 

 identical with itself (fig. 2, p. 339) ; the expressions (14) -are 

 reduced to the form 



COS 



which when integrated gives 



or, 



. 7T , 



cot - ~ 2 



$o being the value of corresponding to t = 0, and K being ex 

 pressed by the following quantity : 



t 



ILL b*ac 



It is evident from the equation (17) that the axis of moments 

 will coincide with the mean axis of inertia at the end of an in- 

 finite time. 



