CENTRE OF GRAVITY. 



229 



being the point of support, the board is in stable equilibrium ; for any motion 

 on either side must cause the centre of gravity C to ascend in the directions 

 C O, and oscillation will ensue. If, however, it rest upon the smaller end, as 

 in fig. 11, the position would still be a state of equilibrium, because the centre 



Fig. 11. 





of gravity is directly above the point of support ; but it would be instable equi- ( 

 librium, because the slightest displacement of the centre of gravity would cause 

 it to descend. 



Thus an egg or a lemon may be balanced on the end ; but the least distur- 

 bance will overthrow it. On the contrary, it will easily rest on the side, and 

 any disturbance will produce oscillation. 



When the circumstances under which the body is placed allow the centre 

 of gravity to move only in a horizontal line, the body is in a state which may 

 be called neutral equilibrium. The slightest force will move the centre of 

 gravity, but will neither produce oscillation nor overthrow the body, as in the 

 last two cases. 



An example of this state is furnished by a cylinder placed upon a horizontal 

 plane. As the cylinder is rolled upon the plane, the centre of gravity C, fig. 

 12, moves in a line parallel to the plane A B, and distant from it by the radius | 



Fig. 12. 



i 

 1 1 



of the cylinder. The body will thus rest indifferently in any position, because 

 the line of direction always falls upon a point P at which the body rests upon 

 the plane. 



If the plane were inclined, as in fig. 13, a body might be so shaped, that, 



