After considering the volume of displacement of ships, the next point to be examined is the shape of the volume as regards stability and steadiness. These two expressions are linked together in the minds of many people as if they were convertible terms. Instead of being so they are in a measure antithetical, as we shall presently see. When a vessel is at rest in still water it is evident that her centre of gravity and the centre of gravity of the volume of water she displaces (which is called the centre of buoyancy) must lie in the same ver tical line, for only in that condition will the forces of weight and buoyancy act in exactly opposite directions and produce equilibrium. The rela tive positions of these points are shown in the accompanying diagrams, in each of which G is the centre of of the ship and B the centre of buoyancy.
tending to turn the ship back to her nprighl position. Similarly, if the ship pitches• th centre of buoyancy is displaced longitudinal) 3 and the couple acts as before. In either case if W is the weight of the ship in tons the ma meat of this couple is equal to W X Gil, oi W X G"H'. If a vessel rolls and pitches al the same time the centre of buoyancy will bt displaced both laterally and longitudinally, anc the couple will then tend to act in a plane, mak. ing an angle with the keel which is greater thar 0 and less than 00 degrees. If a ship is pressei over by a constant force, such as the wind oi the action of the rudder, and the surface of thc water is smooth, the righting moment is simpl3 that of the couple. But if the surface of tht water is broken by waves the shape of the sub merged body is constantly cluing thereby moving the centre of buoyancy and adding to o• sub tracting from the righting force due to the couple. • When a ship is forcibly in clined in still water the point M (Fig. 3), called the transverse metacentre, the point in which the vertical line through B' cuts the line G'31, wide' is vertical when the ship is upright ; and the dis. tance G'M is called the transverse metaeentrii height. Similarly in Fig. 4, M' is the longitudina metaeentre, and G"M' is the longitudinal meta. centric height. In vessels of ordinary type G"M is so large that there is practically no danger ol their turning end over end unless they are ver7 small. G'M, however, is often very small, and its value must he very carefully considered. Being sc much used, it is commonly referred to as OH inetacentrie height. The determination of it is
effected by inclining the ship in still water. It changes for every change in the position of the centre of buoyancy, but for angles not exceeding 15 degrees the change is slight. The value of the metacentric height usually given in tables is, therefore, that obtained by inclining the ship through a very small angle.
The rolling of a ship when forcibly inclined in still water and then allowed to right herself is like that of a pendulum which has been drawn to one side and then permitted to vibrate un til it comes to rest. Acted upon by the couple (the moment of which in this case is called the moment of statical stability), she rapidly reaches the upright position at a constantly varying angular velocity. As soon as this position is reached the couple ceases to act, while her mo mentum causes the roll to continue; but be yond the upright position a couple ill the oppo site direction is formed and this (together with friction and wave-making) gradually checks her roll until it ends. whereupon the new couple sets up a roll in the opposite direction just as a pendulum returns in its vibra tion. The rolling continues, though the arcs arc smaller and smaller each time, the vessel comes to rest ill stable equilibrium in the upright posi tion. The oscillations of a pendulum in vibrating are performed in equal periods of time, irrespective of their amplitude; and this is practically true of the ship, though the wave-making due to the high angular velocity of deep rolls and the in ' creased friction due to greater area of immersed 2 surface cause some variation. The mean length 7 of tulle required for a ship to make a complete • double roll through a moderate angle in smooth water is called the still-water period. In rough r water this period is modified by the action of the waves, which gives a constantly varying value to the total righting moment. If the waves pass I under a ship ill such a way as to add to this moment when the ship is rolling toward tile vertical and reduce it when she is rolling away ' from the vertical, a dangerous condition of :if ' fairs is produced which may result ill her cap sizing. This condition can only exist when the wave period (time between waves) is practically the same as the ship's still-water period; when it does exist the course of the ship with refer - ence to the waves should be materially changed.