230 



CENTRE OF GRAVITY. 



Fig. 13. 



while it would roll, the centre of gravity would move horizontally. In this 

 case, the body would rest indifferently on any part of the plane, as if it were 

 horizontal, provided the friction be sufficient to prevent the body from sliding 

 down the plane. 



If the centre of gravity of a cylinder happen not to coincide with its centre, 

 by reason jof the want of uniformity in the materials of which it is composed, 

 it will not be in a state of neutral equilibrium on a horizontal plane, as in fig. 

 12. In this case, let G, fig. 14, be the centre of gravity. In the position here 

 represented, where the centre of gravity is immediately helow the centre C, the 

 state will be stable equilibrium, because a motion on either side would cause 

 the centre of gravity to ascend; but in fig. 15, where G is immediately above 



Fig. 14. 



Fig. 15. 



C, the state is instable equilibrium, because a motion on either side would 

 cause G to descend, and the body would turn into the position fig. 14. 



A cylinder of this kind will, under certain circumstances, roll up an inclined 

 plane. Let A B, fig. 16, be the inclined plane, and let the cylinder be so 

 placed that the line of direction from G shall be above the point P at which 

 the cylinder rests upon the plane. The whole weight of the body acting in 

 the direction G D will obviously cause the cylinder to roll toward A, provided 

 the friction be sufficient to prevent sliding ; but although the cylinder in this 

 case ascends, the centre of gravity G really descends. 



Fig. 16. 



