Stability with Draught of Water in Ships. 209 



moments, are largely dependent upon the absolute position of the 

 latter point. Speaking generally, it may be said that, keeping 

 the same distance between the metacentre and centre of gravity, 

 the righting moments at successive angles of inclination, and the 

 range of stability, are increased by lowering these points and reduced 

 by raising them. 



Experience proves that some classes of vessels are as safe and 

 seaworthy in respect of stability with 1 foot, or even less, of 

 metacentric height, as others are with 3 or 4 feet; while some of an 

 exceptional character require much greater stability than even the 

 latter figures would give. Examples of this class are to be found 

 among ironclad monitors of very low freeboard and with heavy 

 upper works, including armoured turrets and guns on deck ; and 

 also among paddle steamers of extremely light draught, with 

 extensive tiers of houses above them. These are cases in which the 

 metacentre and centre of gravity are both comparatively high in the 

 ship. 



The vertical position of the metacentre of a floating body is deter- 

 mined by the consideration that the height of the metacentre above 

 the centre of gravity of the volume of displacement is equal to the 

 moment of inertia of the plane of flotation about a longitudinal axis 

 through its centre of gravity divided by the volume of displacement. 



FIG. 2. 



If ABCD (fig. 2) represent the transverse section of a rectangular 

 prismatic body which floats in equilibrium with the side BC hori- 

 zontal, WL the line of flotation, B' the position of the centre of gravity 

 of the displaced volume or centre of buoyancy, and M that of the 

 metacentre, then by Bouguer's well known formula 



-D, moment of inertia of plane of flotation WL 



volume WADL 



Let AB=a, BC=6, and WA, the depth of flotation d. The 

 moment of inertia of an unit of length of the water-line plane 



VOL. XXXVII. P 



