of a rigid Body round ajixed Point. 



44-1 



Again, if the plane of the impressed moment intersects the 

 mean plane between Nand C, it will envelope the cone whose 



focals are ON, ON'; but if the plane of the impressed mo- 

 ment intersect between A and N, it will envelope the cone 

 whose focals are O N, O M ; hence the range in the former 

 case, which may be taken as the measure of the stability of 

 rotation round the principal axe whose moment of inertia is 

 greatest, is to the range in the latter, which may be deemed 

 the representative of the stability round the axis whose mo- 

 ment of inertia is the least, as the supplement of the angle 

 between the optic axes, or between the circular sections of 

 the ellipsoid is to the angle itself. 



XIX. In the particular case, where the plane of the im- 

 pressed moment passes through the optic axe of the ellipsoid, 

 the cones become portions of the plane of the greatest and 

 least axes of the surface, divided one from the other by the 

 optic axes ; hence if the plane of the impressed moment be 

 disturbed from coincidence with the mean plane of the ellip- 

 soid, so as to commence its rotation round one of the optic 

 axes, it will either return to its former position of coincidence, 

 or revolve through 180° round the optic axe, till it coincides 

 at length with the mean plane on the opposite side ; hence 

 the axe of the impressed moment must revolve in a circular 

 section of the ellipsoid, through an angle less than 180°, with 

 a variable velocity, till it at length coincides with the mean 

 axe of the ellipsoid, the body in the mean time uniformly re- 

 volving round this axe so moving in the circular section. 



[To be continued.] 



