STABILITY AND 'I/STABILITY. When a body rests upon a sprface in such a man ner that a vertical lrom its center of gravity falls within the largest polygon which can be formed by joining the various points of contact of base and surface, it will stand; but if the contrary is the case, it will fall, unless extraneously supported. If the base of the body be a plane, and the supporting surface convex, or vice versa, or if boils base and surface be convex, there will be only one point of support, and if the body be at rest, its center of gravity must be verti cally over the point of contact. Should a body so placed receive a slight Impulse, it will either oscillate to and fro, ultimately returning to its original position, or remove further and further from its original posi tion, showing a tendency not to return, or appear indif ferent to any one position. In the first case, the body is said to be in stable, in the second case, in unstable, and in the third, in neutral equilibrium. Fig. 1 shows various illustrations of these Aimee species. It will appear at once that the predetermining cause of equi librium being of one rather than of another of thesd species, is the tendency of the center of gravity of gravityevery body to seek a lower position. In stable
brium the center of gravity of the body may, and in attain a lower position, while in neutral equilibrium its unstable equilibrium may not, position continues unaltered. In illustration of the mode in which the specks of equili brium possessed by a body which has received a slight impulse is determined, let us take the case of a body with a spherical base resting upon a spherical surface (fig. 1); let S and 0 be the centers of the spherical surfaces respectively, and let A be their point of contact (the center of gravity being consequently in ihe line SA, or in it produced toward 5, and after displacement, in the line SA', produced if necessary). let the new position of S, after the body has been slightly displaced, be S', and the new point of contact B; join OS, OS', Si',• and draw III) vertically, that is, parallel to OC. Then x OB