Stability with Drauykt of Water in Skips. 



207 



position of equilibrium, with the vertical through the centre of gravity 

 of the displaced volume in the original position of equilibrium.* 



FIG. 1. 



For instance, if AEF in fig. 1 represent the transverse section of a 

 ship upon which WL is the intersection of the water-line plane when 

 the vessel is upright and in a position of equilibrium, and B the 

 position of the centre of gravity of the volume of displacement 

 W AL or centre of buoyancy as it is commonly called ; and if AH be 

 the vertical through B when the vessel is floating in equilibrium at 

 the water-line "WL, then if the vessel be inclined through a small 

 angle WOWj, and the point Bj represent the centre of buoyancy of 

 the immersed volume WjAL^, the vertical BjM, drawn through B 1? 

 will intersect the original vertical AH in a point M. M is the meta- 

 centre when the angle of inclination WOW\ is indefinitely small. It 

 then represents the ultimate intersection of the new vertical through 

 Bj with the original vertical BH. In a ship the vertical correspond- 

 ing to the upright position of equilibrium is, for all practical purposes, 

 the intersection AH of the middle line longitudinal plane with the 

 transverse section. 



Bouguer showed that the position of the metacentre limits the 

 height to which the centre of gravity of a floating body may be 

 raised without making it unstable, and that the righting moments 

 at small angles of inclination from a position of stable equilibrium 

 are proportional to the height of the metacentre above the centre of 

 gravity. This is readily seen, because if Gr in fig. 1 be the position of 

 the centre of gravity of a ship, and GrZ the horizontal distance between 



* It is a moot question whether the term metacentre should not be made to 

 embrace all the ultimate intersections of consecutive verticals through the centres of 

 gravity of the displaced volume. Bouguer calls the locus of such intersections 

 the metacentrique. 



