(161.) The two states of equilibrium which have been just noticed, are called stable and instable equilibrium. The character of the former is, that any disturbance of the state produces oscillation about it; but any disturbance of the latter state produces a total overthrow, and finally causes oscillation around the state of stable equilibrium. Let A B, _fig. 45._, be an elliptical board resting on its edge on an horizontal plane. In the position here represented, the extremity P of the lesser axis 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. 46._, the position would still be a state of equilibrium, because the centre of gravity is directly above the point of support; but it would be instable equilibrium, 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 disturbance will overthrow it. On the contrary, it will easily rest on the side, and any disturbance will produce oscillation. (162.) When the circumstances under which the body is placed allow the centre of gravity to move only in an 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 an horizontal plane. As the cylinder is rolled upon the plane, the centre of gravity C, _fig. 47._, moves in a line parallel to the plane A B, and distant from it by the radius 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. 48._, a body might be so shaped, that 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 of the want of uniformity in the materials of which it is composed, it will not be in a state of neutral equilibrium on an horizontal plane, as in _fig. 47._ In this case let G, _fig. 49._, be the centre of gravity. In the position here represented, where the centre of gravity is immediately _below_ 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. 50._, where G is immediately above 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. 49._