(163.) A cylinder of this kind will, under certain circumstances, roll up an inclined plane. Let A B, _fig. 51._, 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 towards A, provided the friction be sufficient to prevent sliding; but although the cylinder in this case ascends, the centre of gravity G really descends. When G is so placed that the line of direction G D shall fall on the point P, the cylinder will be in equilibrium, because its weight acts upon the point on which it rests. There are two cases represented in _fig. 52._ and _fig. 53._, in which G takes this position. _Fig. 52._ represents the state of stable, and _fig. 53._ of instable equilibrium. (164.) When a body is placed upon a base, its stability depends upon the position of the line of direction and the height of the centre of gravity above the base. If the line of direction fall within the base, the body will stand firm; if it fall on the edge of the base, it will be in a state in which the slightest force will overthrow it on that side at which the line of direction falls; and if the line of direction fall without the base, the body must turn over that edge which is nearest to the line of direction. In _fig. 54._ and _fig. 55._, the line of direction G P falls within the base, and it is obvious that the body will stand firm; for any attempt to turn it over either edge would cause the centre of gravity to ascend. But in _fig. 56._ the line of direction falls upon the edge, and if the body be turned over, the centre of gravity immediately commences to descend. Until it be turned over, however, the centre of gravity is supported by the edge. In _fig. 57._ the line of direction falls outside the base, the centre of gravity has a tendency to descend from G towards A, and the body will accordingly fall in that direction. (165.) When the line of direction falls within the base, bodies will always stand firm, but not with the same degree of stability. In general, the stability depends on the height through which the centre of gravity must be elevated before the body can be overthrown. The greater this height is, the greater in the same proportion will be the stability. Let B A C, _fig. 58._, be a pyramid, the centre of gravity being at G. To turn this over the edge B, the centre of gravity; must be carried over the arch G E, and must therefore be raised through the height H E. If, however, the pyramid were taller relatively to its base, as in _fig. 59._, the height H E would be proportionally less; and if the base were very small in reference to the height, as in _fig. 60._, the height H E would be very small, and a slight force would throw it over the edge B.