MECHANICS OF LIQUIDS 79 



body, G, and the center of buoyancy of the water, B, is 

 vertical, and is called the axis of equilibrium. When an 

 external force causes the axis of equilibrium to lean, if a 

 vertical line is drawn upward from the center of buoyancy 

 to this axis, the point where it cuts the axis is called the meta- 

 center. If the metacenter is above the center of gravity 

 the distance between them is called the metacenter height, 

 and the body is then said to be in stable equilibrium, that is, 

 tending to return to its original position, when the external 

 force is removed. 



79. Stability of a Ship. A ship at sea is subject to rolling 

 and pitching and must be designed to be stable and not 

 capsize. Rolling is the motion of a ship from side to side. 

 Pitching is the alternate rising and falling of bow and stern. 

 In general a ship's motion is a combination of rolling and 

 pitching. The principle of hydrostatics (water pressure) 

 governing the stability is as follows: When a ship is floating 

 at rest its center of gravity and its center of buoyancy are 

 in the same vertical line. If the force of winds or waves 

 causes the vessel to keel over as in Fig. 51, the weight of 

 the ship W acting downward through G, and her buoyancy 

 acting upward through B constitute a couple* which tends to 

 pull the ship back again upon an even keel with a turning 

 moment equal to W X GP. If the couple be strong enough 

 the ship will swing back towards an even keel. But since 

 the vessel acquires kinetic energy as it swings, it will not 



* A couple is composed of two equal parallel forces acting on the 

 ends of a bar, for example, in opposite directions ; so far as producing 

 forward or backward motion is concerned their resultant is zero. 

 They do, however, tend to cause the bar to rotate. 



