motion acquired by the body in its descent from the first position has been destroyed, and then it will begin to return to P F, and so it will continue to vibrate from the one side to the other until the friction on the point P, and the resistance of the air, gradually deprive it of its motion, and bring it to a state of rest in the direction P F. But for the effects of friction and atmospheric resistance, the body would continue for ever to oscillate equally from side to side of the line P F. (159.) The phenomenon just developed is only an example of an extensive class. Whenever the circumstances which restrain the body are of such a nature that the centre of gravity is prevented from descending below a certain level, but not, on the other hand, restrained from rising above it, the body will remain at rest if the centre of gravity be placed at the lowest limit of its level; any disturbance will cause it to oscillate around this state, and it cannot return to a state of rest until friction or some other cause have deprived it of the motion communicated by the disturbing force. (160.) Under the circumstances which we have just described, the body could not maintain itself in a state of rest in any position except that in which the centre of gravity is, at the lowest point of the space in which it is free to move. This, however, is not always the case. Suppose it were suspended by an inflexible rod instead of a flexible string; the centre of gravity would then not only be prevented from receding from the point of suspension, but also from approaching it; in fact, it would be always kept at the same distance from it. Thus, instead of being capable of moving anywhere within the sphere, it is now capable of moving on its surface only. The reasoning used in the last case may also be applied here, to prove that when the centre of gravity is on either side of the perpendicular P F, it will fall towards P F and oscillate, and that if it be placed in the line P F, it will remain in equilibrium. But in this case there is another position, in which the centre of gravity may be placed so as to produce equilibrium. If it be placed at the highest point of the sphere in which it moves, the whole force acting on it will then be directed on the point of suspension, perpendicularly downwards, and will be entirely expended in producing pressure on that point; consequently, the body will in this case be in equilibrium. But this state of equilibrium is of a character very different from that in which the centre of gravity was at the lowest part of the sphere. In the present case any displacement, however slight, of the centre of gravity, will carry it to a lower level, and the force of gravity will then prevent its return to its former state, and will impel it downwards until it attain the lowest point of the sphere, and round that point it will oscillate.