MECHANICS. 145 



their velocities, and their distances from the axis 

 of motion, is equal to the momentum of the force 

 impressed, estimated in the same manner* 



Hence, though, in consequence of the rotation of a 

 body on its axis, a change may take place in its 

 figure, or in its internal structure, the total quantity 

 of its momentum will continue the same, 



227 A body may begin to revolve on any line as 

 an axis, which passes through its centre of gravity, 

 but it will not continue to revolve permanently 

 about that axis, unless the opposite centrifugal 

 forces exactly balance one another. 



A homogeneous sphere may revolve permanently on 

 any diameter, because the opposite parts of the so- 

 lid, being in every direction equal and similar, the 

 opposite centrifugal forces must be equal ; so that 

 no force tends to change the position of the axis. 



A homogeneous cylinder may revolve permanently 

 about the line which is its geometric axis. It may 

 also revolve permanently about any line that bisects 

 that axis at right angles ; but it can revolve perma- 

 nently about no other line, as the centrifugal forces 

 cannot be equal. The same is true with respect to 

 all solids of revolution. 



228. In every body, however irregular, there 



are three axes of permanent rotation, at right 



VOL. I. K angles 



