METACENTRE ( from Gk. pera, meta, after Kivrpov, kentron, centre). It is shown in hydro statics that a floating, body is acted on by two equal forces in opposite directions; one, vertically down through the centre of gravity of the body itself; the other, vertically up through the of gravity of the volume which was occupied by the liquid now displaced by the body. If the body is at rest, these two forces must lie in the same vertical line; hut the question of the sta bility of this equilibrium depends upon what happens when the floating body is tipped slight ly. If the forces bring it back to its former posi tion, the equilibrium is stable; if they make it tip still farther, the equilibrium is unstable. Imagine a line drawn in the floating body so as to pass through the centres of gravity of the body and of the displaced liquid, when the body is in equilibrium; this line is called the `axis.' Now imagine the body tipped slightly, thus mak ing the axis inclined to the vertical ; the line of action of the vertical upward force will intersect this line at a point called the `metacentre.' if
the metacentre lies above the centre of gravity of the body, the two forces will form a couple tending to restore the body to its former posi tion, where the equilibrium was stable. If, on the other hand, the metacentre is below the centre of gravity of the body. the forces form a couple tending to tip the body farther, and so the equilibrium was unstable. An elongated floating body like a ship has a transverse metacentre and a longitudinal metacentre. The former is the one most commonly considered. The metacentric height is the vertical distance between the centre of gravity and the metacentre. It is evident that this must always he a positive quantity; for if the centre of gravity were above the metacentre there would be no force tending to keep the ves sel upright and it would capsize. See Sulu BUILDING.